How to find the area of an acute / obtuse triangle - GRE Quantitative Reasoning

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.

The question doesn't tell us if this is a right triangle, so we can't assume that it is. But there is a formula to find the area when we don't know the height: area = \[p(p – a)(p – b)(p – c)\]1/2, where a, b, and c are the side lengths and p is half of the perimeter. The perimeter is 18 + 24 + 30 = 72, so p = 72/2 = 36.

Then area = \[36(36 – 18)(36 – 24)(36 – 30)\]1/2 = \[36 * 12 * 6 * 18\]1/2 = 216.

Since we are told nothing about the angles we cannot assume that these are isosceles triangles and are open to possibilites such as that shown below in which the left side would be larger. If both were isosceles triangles then the right side would be larger.