Calculating the length of the side of a right triangle - 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.

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

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 .

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 and the longer side as . Then we are able to set up an equation:

.

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

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.

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

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 .

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 and the longer side as . Then we are able to set up an equation:

.

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

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.

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: