Question

In a right triangle, the length of the hypotenuse is 20 inches and the length of one leg is 15 inches. What is the length of the other leg in inches? A. 5√ 7 B. 5 C. 25 D. √ 7

Answer 1

Well the normal way to go about solving sides of right triangles is by the Pythagorean Theorem:

`{a}^(2) + {b}^(2) = {c}^(2)`
where a and b are the two smaller sides and c is always the hypotenuse.
So if we make b = 15 in, c = 20 in, a = ??

`{a}^(2) + {b}^(2) = {c}^(2) \\ {a}^(2) = {c}^(2) - {b}^(2) \\ \sqrt{ {a}^(2)} = \sqrt{( {c}^(2) - {b}^(2)) } \\ a = \sqrt{( {c}^(2) - {b}^(2)) }`
Now plug-in for b and c:

`a = \sqrt{( {c}^(2) - {b}^(2)) } \\ a = \sqrt{( {20}^(2) - {15}^(2)) } \\ a = √((400 - 225) ) = √(175) \\ a = √(25) * √(7) = 5 √(7) \: in`