What are the dimensions of an isosceles right triangle with a four-inch hypotenuse and an area of 4 square inches?
A) $$2 \sqrt { 2 }$$ in.× $$2 \sqrt { 2 }$$ in.× 4 in.
B) $\sqrt { 10 }$ in.× $\sqrt { 10 }$ in.× 4 in.
C) $3$ in.× $3$ in.× 4 in.
D) $\sqrt { 11 }$ in.× $\sqrt { 11 }$ in.× 4 in.
E) $2 \sqrt { 3 }$ in.× $2 \sqrt { 3 }$ in.× 4 in.

Question

What are the dimensions of an isosceles right triangle with a four-inch hypotenuse and an area of 4 square inches? ​
A) $$2 \sqrt { 2 }$$ in.× $$2 \sqrt { 2 }$$ in.× 4 in.
B) $\sqrt { 10 }$ in.× $\sqrt { 10 }$ in.× 4 in.
C) $3$ in.× $3$ in.× 4 in.
D) $\sqrt { 11 }$ in.× $\sqrt { 11 }$ in.× 4 in.
E) $2 \sqrt { 3 }$ in.× $2 \sqrt { 3 }$ in.× 4 in.

Quizplus · Accepted Answer

In an isosceles right triangle, the legs are equal, and the hypotenuse is $\sqrt{2}$ times longer than each leg. Given a hypotenuse of 4 inches, each leg is $4/\sqrt{2} = 2\sqrt{2}$ inches. The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$, and since the base and height are the legs of the triangle, the area calculation confirms the dimensions are correct for an area of 4 square inches.

What Are the Dimensions of an Isosceles Right Triangle with a Four-Inch