Calculating the height of a right triangle - GMAT Quantitative

The hypotenuse of the large right triangle is

The area of the large right triangle is half the product of its base and its height. The base can be any side of the triangle; the height would be the length of the altitude, which is the perpendicular segment from the opposite vertex to that base.

Therefore, the area of the triangle can be calculated as half the product of the legs:

Or half the product of the hypotenuse and the length of the dashed line.

To calculate , we can set these expressions equal to each other:

Using the formula for the area of a right triangle, we can plug in the given values and solve for the height of the triangle:

The height AE, divides the triangle ABC, in two triangles AEC and AEB with same proportions as the original triangle ABC, this property holds true for any right triangle.

In other words, .

Therefore, we can calculate, the length of AE:

.

As we have previously seen, the height of a right triangle divides a it into two similar triangles with sides of same proportion.

Therefore, we can set up the following equality: or .

By plugging in the numbers, we get, or .

The hypotenuse of the large right triangle is

The area of the large right triangle is half the product of its base and its height. The base can be any side of the triangle; the height would be the length of the altitude, which is the perpendicular segment from the opposite vertex to that base.

Therefore, the area of the triangle can be calculated as half the product of the legs:

Or half the product of the hypotenuse and the length of the dashed line.

To calculate , we can set these expressions equal to each other:

Using the formula for the area of a right triangle, we can plug in the given values and solve for the height of the triangle:

The height AE, divides the triangle ABC, in two triangles AEC and AEB with same proportions as the original triangle ABC, this property holds true for any right triangle.

In other words, .

Therefore, we can calculate, the length of AE:

.

As we have previously seen, the height of a right triangle divides a it into two similar triangles with sides of same proportion.

Therefore, we can set up the following equality: or .

By plugging in the numbers, we get, or .

Since here ABC is a isosceles right triangle, its height is half the size of the hypotenuse.

We just need to apply the Pythagorean Theorem to get the length of BC, and divide this length by two.

, so .

Therefore, and the final answer is .

Since here ABC is a isosceles right triangle, its height is half the size of the hypotenuse.

We just need to apply the Pythagorean Theorem to get the length of BC, and divide this length by two.

, so .

Therefore, and the final answer is .

The hypotenuse of the large right triangle is

The area of the large right triangle is half the product of its base and its height. The base can be any side of the triangle; the height would be the length of the altitude, which is the perpendicular segment from the opposite vertex to that base.

Therefore, the area of the triangle can be calculated as half the product of the legs:

Or half the product of the hypotenuse and the length of the dashed line.

To calculate , we can set these expressions equal to each other:

Using the formula for the area of a right triangle, we can plug in the given values and solve for the height of the triangle:

The height AE, divides the triangle ABC, in two triangles AEC and AEB with same proportions as the original triangle ABC, this property holds true for any right triangle.

In other words, .

Therefore, we can calculate, the length of AE:

.

As we have previously seen, the height of a right triangle divides a it into two similar triangles with sides of same proportion.

Therefore, we can set up the following equality: or .

By plugging in the numbers, we get, or .

The hypotenuse of the large right triangle is

The area of the large right triangle is half the product of its base and its height. The base can be any side of the triangle; the height would be the length of the altitude, which is the perpendicular segment from the opposite vertex to that base.

Therefore, the area of the triangle can be calculated as half the product of the legs:

Or half the product of the hypotenuse and the length of the dashed line.

To calculate , we can set these expressions equal to each other:

Using the formula for the area of a right triangle, we can plug in the given values and solve for the height of the triangle:

The height AE, divides the triangle ABC, in two triangles AEC and AEB with same proportions as the original triangle ABC, this property holds true for any right triangle.

In other words, .

Therefore, we can calculate, the length of AE:

.

As we have previously seen, the height of a right triangle divides a it into two similar triangles with sides of same proportion.

Therefore, we can set up the following equality: or .

By plugging in the numbers, we get, or .

Since here ABC is a isosceles right triangle, its height is half the size of the hypotenuse.

We just need to apply the Pythagorean Theorem to get the length of BC, and divide this length by two.

, so .

Therefore, and the final answer is .