Right Triangles - GMAT Quantitative

This triangle can exist by the Triangle Inequality, since the sum of the lengths of its shortest two sides exceeds that of the longest side:

The sum of the squares of its shortest two sides is less than the square of that of its longest side:

This makes the triangle obtuse.

Its sides are all of different measure, which makes the triangle scalene as well.

Obtuse and scalene is the correct choice.

The area of the big square is 5, and area of the small square is 1. Therefore, the area of the four right triangles is 5-1=4.

Since the four triangles are all exactly the same, the area of each of the right triangle is 1. We know that the longer side is 2 times the shorter side, so we can represent the shorter side as x and the longer side as 2x. Then we are able to set up an equation:

$\frac{1}{2}$times xtimes 2x=1.

Therefore, x, the length of the shortest side of the right triangle, is 1.

We need to use the Pythagorean theorem:

We can determine the length of the side by using the Pythagorean Theorem:

where

Our equation is then:

We can calculate the length of the side by using the pythagorean theorem:

where our values are

we can then solve for :

In order to find the length of the third side, we need to use the Pythagorean theorem. The hypotenuse, c, is 13, and the height, a, is 5, so we can simply plug in these values and solve for b, the length of the base of the right triangle:

The shortest leg of a triangle is one half the length of its hypotenuse. In this triangle, it is

A triangle is a right triangle. To find the perimeter, we must add up all the sides of the triangle.

The hypotenuse of a 30-60-90 triangle measures twice its shorter leg; its longer leg measures times its shorter leg. Given one side length alone, there is no indication which of the three sides it measures; but given two, one of which is twice the other, as is the case here (10 and 20), 10 must be the shorter leg and 20 the hypotenuse. The longer leg is therefore , and the perimeter is

.

Therefore, both statements together are sufficent but neither alone is sufficient.

We can use the Pythagorean Theorem to calculate the hypotenuse of the triangle by setting in this formula:

The perimeter is feet.

Divide by 3 to convert to yards:

yards

We can use the Pythagorean Theorem to calculate the length of the second leg in yards of the triangle by setting in this formula:

The perimeter of the triangle is yards is

yards. Multiply this by 36 to covert to inches:

inches.

We are given two sides of the right triangle, so in order to calculate the perimeter we must first find the length of the third side, the hypotenuse, using the Pythagorean theorem:

Now that we know the length of the third side, we can add the lengths of the three sides to calculate the perimeter of the right triangle:

As you see that a right triangle as sides 3 and 4, you should always remember that, this right triangle is a Pythagorean Triple, in other words, its sides will be in the ratio where is a constant, this will save you a lot of time. Here we can say that the hypotenuse will be 5. Therefore, the circumference will be . To get the final answer, we should just divide the circumference by 2 and add the perimeter, being or 12.

For starters, we know that the hypotenuse is the longest side of a triangle, so we can immediately cross off 25 as an answer choice because it is smaller than one of the legs, 48. To find the hypotenuse, we can use the Pythagorean Theorem.

$hypotenuse^{^{2}$} = $14^{2}$ + $48^{2}$ = 2500

hypotenuse = 50

To find a length of a side in a right triangle, we can use the Pythagorean theorem:

We are given the length of the height and the base, so we can use the Pythagorean theorem to calculate the length of the hypotenuse:

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem:

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem:

In order to find the value of the hypotenuse given area and leg length , we first need to calculate the length of the other leg length . Given the area equation :

Plugging in and :

Now we need to plug the values of the legs and into the Pythagorean Theorem:

The hypotenuse of a triangle has length times that of a leg, which here is

.