ISEE Upper Level Quantitative : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem
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Example Questions
Example Question #11 : Right Triangles
Figure NOT drawn to scale.
In the above figure, 
What is the length of 
The altitude of a right triangle from the vertex of its right angle divides the triangle into two smaller triangles each similar to the larger triangle. In particular,
Their corresponding sides are in proportion, so, setting the ratios of the long legs to the short legs equal to each other,
By the Pythagorean Theorem.
The proportion statement becomes
Example Question #12 : Right Triangles
Given: 
Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(a) is the greater quantity
(a) is the greater quantity
The measure of the angle formed by the two shorter sides of a triangle can be determined to be acute, right, or obtuse by comparing the sum of the squares of those lengths to the square of the length of the opposite side. We compare:
Example Question #13 : Right Triangles
Figure NOT drawn to scale.
In the above figure, 
What is the length of 
The altitude of a right triangle from the vertex of its right angle divides the triangle into two smaller triangles each similar to the larger triangle. In particular,
Their corresponding sides are in proportion, so, setting the ratios of the hypotenuses to the short legs equal to each other,
All ISEE Upper Level Quantitative Resources
