Write the specified quantity as a function of the specified variable.
-One leg of a right triangle is three times as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.
A) $c = 2 a$
B) $c = 10 a ^ { 2 }$
C) $c = 2 \sqrt { a }$
D) $c = a \sqrt { 10 }$

Question

Quizplus · Accepted Answer

Given a right triangle where one leg is three times as long as the other, let the shorter leg be $a$ and the longer leg be $3a$. By the Pythagorean theorem, $c^2 = a^2 + (3a)^2 = a^2 + 9a^2 = 10a^2$, so $c = a\sqrt{10}$.

Write the Specified Quantity as a Function of the Specified c=2ac = 2 ac=2a

Write the Specified Quantity as a Function of the Specified $c = 2 a$