SAT Area and volume Practice Question 3 (Medium)

Math · Geometry and TrigonometryMedium

A right triangle has legs of length $9$ and $12$ . A square has the same area as the triangle. What is the side length of the square?

$7.5$

$6\sqrt{3}$

$27$

$3\sqrt{6}$

Show answer and explanation

Answer: D

The area of the triangle is $\frac{1}{2}(9)(12) = 54$ . A square with area $54$ has side length $\sqrt{54} = \sqrt{9 \cdot 6} = 3\sqrt{6}$ .

Choice B is $\sqrt{108}$ , which comes from forgetting the $\frac{1}{2}$ in the triangle area formula.

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