For this problem use the isosceles right triangle in the figure. If c = 16 meters find a and b . Express the answers in simplest radical form.
A) $a = 8 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$
B) $a = 16 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$
C) $a = 8 \text { meters, } b = 8 \text { meters }$
D) $a = 8 \sqrt { 2 } \text { meters, } b = 8 \sqrt { 2 } \text { meters }$

Question

For this problem use the isosceles right triangle in the figure. If c = 16 meters find a and b . Express the answers in simplest radical form. 
A) $a = 8 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$ 
B) $a = 16 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$ 
C) $a = 8 \text { meters, } b = 8 \text { meters }$ 
D) $a = 8 \sqrt { 2 } \text { meters, } b = 8 \sqrt { 2 } \text { meters }$

Quizplus · Accepted Answer

In an isosceles right triangle with legs of length $a$, the hypotenuse is $a\sqrt{2}$. Since the hypotenuse in this case is 16, we have $a\sqrt{2}=16$, or $a=8\sqrt{2}$. Therefore, both legs have length $8\sqrt{2}$, so the correct answer is D.

For This Problem Use the Isosceles Right Triangle in the Figure