Solve.
-An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.
A) $\frac { 11 } { 2 } \sqrt { 2 } \mathrm { in }$.
B) $22 \sqrt { 2 } \mathrm { in }$.
C) $121 \sqrt { 2 } \mathrm { in }$.
D) $11 \sqrt { 2 } \mathrm { in }$.

Question

Quizplus · Accepted Answer

In an isosceles right triangle, the legs are equal, and the hypotenuse is $\sqrt{2}$ times longer than each leg. Using the Pythagorean theorem, if $x$ is the length of each leg, then $x^2 + x^2 = 22^2$. Simplifying, $2x^2 = 484$, so $x^2 = 242$, and $x = \sqrt{242} = 11\sqrt{2}$.

Solve -An Isosceles Right Triangle Has Legs of Equal Length 1122in\frac { 11 } { 2 } \sqrt { 2 } \mathrm { in }211​2​in

Solve
-An Isosceles Right Triangle Has Legs of Equal Length $\frac { 11 } { 2 } \sqrt { 2 } \mathrm { in }$