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SSAT Upper Level Math : How to find the height of an acute / obtuse triangle

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #591 : Geometry

The area of a triangle is 240 $\displaystyle 240$, and the base of the triangle is $\displaystyle 30$. What is the height for this triangle?

Possible Answers:

$\displaystyle 24$

$\displaystyle 16$

$\displaystyle 8$

$\displaystyle 32$

Correct answer:

$\displaystyle 16$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$240=\frac{30 \times h}{2}$ $\displaystyle 240=\frac{30 \times h}{2}$

480=30h $\displaystyle 480=30h$

h=16 $\displaystyle h=16$

The height of the triangle is $\displaystyle 16$.

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 360m^2 $\displaystyle 360m^2$ and a base of 60m $\displaystyle 60m$. In meters, find the height.

Possible Answers:

18m $\displaystyle 18m$

24m $\displaystyle 24m$

$\displaystyle 6m$

12m $\displaystyle 12m$

Correct answer:

12m $\displaystyle 12m$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$360=\frac{60\times h}{2}$ $\displaystyle 360=\frac{60\times h}{2}$

720=60h $\displaystyle 720=60h$

h=12 $\displaystyle h=12$

The height of the triangle is $\displaystyle 12$ meters.

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Example Question #61 : Acute / Obtuse Triangles

A triangle has an area of $\displaystyle 45$ and a base of $\displaystyle 15$. Find the height.

Possible Answers:

$\displaystyle 12$

$\displaystyle 9$

$\displaystyle 3$

$\displaystyle 6$

Correct answer:

$\displaystyle 6$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$45=\frac{15\times h}{2}$ $\displaystyle 45=\frac{15\times h}{2}$

90=15h $\displaystyle 90=15h$

h=6 $\displaystyle h=6$

The height of the triangle is $\displaystyle 6$.

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of $\displaystyle 24$ and a base of $\displaystyle 12$. Find the height.

Possible Answers:

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 2$

$\displaystyle 8$

Correct answer:

$\displaystyle 4$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$24=\frac{12\times h}{2}$ $\displaystyle 24=\frac{12\times h}{2}$

48=12h $\displaystyle 48=12h$

h=4 $\displaystyle h=4$

The height of the triangle is $\displaystyle 4$.

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Example Question #153 : Properties Of Triangles

A triangle has an area of $\displaystyle 54$ and a base of $\displaystyle 12$. Find the height.

Possible Answers:

$\displaystyle 15$

$\displaystyle 18$

$\displaystyle 12$

$\displaystyle 9$

Correct answer:

$\displaystyle 9$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$54=\frac{12\times h}{2}$ $\displaystyle 54=\frac{12\times h}{2}$

108=12h $\displaystyle 108=12h$

h=9 $\displaystyle h=9$

The height of the triangle is $\displaystyle 9$.

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Example Question #154 : Properties Of Triangles

A triangle has an area of $\displaystyle 60$ and a base of $\displaystyle 12$. Find the height.

Possible Answers:

$\displaystyle 10$

$\displaystyle 5$

$\displaystyle 20$

$\displaystyle 15$

Correct answer:

$\displaystyle 10$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$60=\frac{12\times h}{2}$ $\displaystyle 60=\frac{12\times h}{2}$

120=12h $\displaystyle 120=12h$

h=10 $\displaystyle h=10$

The height of the triangle is $\displaystyle 10$.

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Example Question #2 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 24x^2 $\displaystyle 24x^2$ and a base of $\displaystyle 6x$. In terms of $\displaystyle x$, find the height.

Possible Answers:

$\displaystyle 6x$

10x $\displaystyle 10x$

$\displaystyle 4x$

$\displaystyle 8x$

Correct answer:

$\displaystyle 8x$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$24x^2=\frac{6x\times h}{2}$ $\displaystyle 24x^2=\frac{6x\times h}{2}$

$\displaystyle 48x^2=6x(h)$

$h=\frac{48x^2}{6x}=8x$ $\displaystyle h=\frac{48x^2}{6x}=8x$

The height of the triangle is $\displaystyle 8x$.

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 128y^2 $\displaystyle 128y^2$ and a base of 16y $\displaystyle 16y$. In terms of $\displaystyle y$, find the height.

Possible Answers:

12y $\displaystyle 12y$

16y $\displaystyle 16y$

20y $\displaystyle 20y$

$\displaystyle 8y$

Correct answer:

16y $\displaystyle 16y$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$128y^2=\frac{16y\times h}{2}$ $\displaystyle 128y^2=\frac{16y\times h}{2}$

$\displaystyle 256y^2=16y(h)$

h=16y $\displaystyle h=16y$

The height of the triangle is 16y $\displaystyle 16y$.

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 48a $\displaystyle 48a$ and a base of $\displaystyle 6a$. What is the height?

Possible Answers:

$\displaystyle 8a$

16a $\displaystyle 16a$

$\displaystyle 8$

$\displaystyle 16$

Correct answer:

$\displaystyle 16$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$48a=\frac{6a\times h}{2}$ $\displaystyle 48a=\frac{6a\times h}{2}$

$\displaystyle 96a=6a(h)$

$h=\frac{96a}{6a}=\frac{96}{6}=16$ $\displaystyle h=\frac{96a}{6a}=\frac{96}{6}=16$

The height of the triangle is $\displaystyle 16$.

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 56t $\displaystyle 56t$ and a base of $\displaystyle 7t$. Find the height.

Possible Answers:

$\displaystyle 16$

$\displaystyle 8$

$\displaystyle 8t$

16t $\displaystyle 16t$

Correct answer:

$\displaystyle 16$

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height $\displaystyle h$.

$56t=\frac{7t\times h}{2}$ $\displaystyle 56t=\frac{7t\times h}{2}$

$\displaystyle 112t=7t(h)$

$h=\frac{112t}{7t}=\frac{112}{7}=16$ $\displaystyle h=\frac{112t}{7t}=\frac{112}{7}=16$

The height of the triangle is $\displaystyle 16$.

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SSAT Upper Level Math : How to find the height of an acute / obtuse triangle

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #591 : Geometry

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #61 : Acute / Obtuse Triangles

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #153 : Properties Of Triangles

Example Question #154 : Properties Of Triangles

Example Question #2 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

All SSAT Upper Level Math Resources

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