Calculating the length of the side of a right triangle - GMAT Quantitative Reasoning
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There is a big square that consists of four identical right triangles and a small square. If the area of the small square is 1, the area of the big square is 5, what is the length of the shortest side of the right triangles?
There is a big square that consists of four identical right triangles and a small square. If the area of the small square is 1, the area of the big square is 5, what is the length of the shortest side of the right triangles?
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.
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
Therefore, x, the length of the shortest side of the right triangle, is 1.
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A triangle has sides of length 9, 12, and 16. Which of the following statements is true?
A triangle has sides of length 9, 12, and 16. Which of the following statements is true?
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.
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.
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What is the side length of a right triangle with a hypotenuse of 
and a side of 
?
What is the side length of a right triangle with a hypotenuse of
We need to use the Pythagorean theorem:
We need to use the Pythagorean theorem:
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Using the following right traingle, calculate the value of 
(Not drawn to scale.)
Using the following right traingle, calculate the value of
(Not drawn to scale.)
We can determine the length of the side by using the Pythagorean Theorem:
where 
Our equation is then:
We can determine the length of the side by using the Pythagorean Theorem:
where
Our equation is then:
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Calculate the length of the side of the following right triangle.
(Not drawn to scale.)
Calculate the length of the side of the following right triangle.
(Not drawn to scale.)
We can calculate the length of the side by using the pythagorean theorem: 
where our values are 
we can then solve for 
:
We can calculate the length of the side by using the pythagorean theorem:
where our values are
we can then solve for
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A right triangle has a hypotenuse of 13 and a height of 5. What is the length of the third side of the triangle?
A right triangle has a hypotenuse of 13 and a height of 5. What is the length of the third side of the triangle?
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:
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:
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The hypotenuse of a 
triangle has length 
. Which of the following is equal to the length of its shortest leg?
The hypotenuse of a
The shortest leg of a 
triangle is one half the length of its hypotenuse. In this triangle, it is
The shortest leg of a
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