Question

The legs of a right triangle measure $\sqrt[5]{2}$ cm and $\sqrt[4]{2}$ cm.

Find the area.

A. $\sqrt[10]{2}$ sq. cm

B. 20 sq. cm

C. $\sqrt[20]{2}$ sq. cm

Answer 1

Answer:

B. 20 sq. cm

Step-by-step explanation:

Given:

The legs of a right triangle measure:

$5\sqrt{2}\ cm$ and $4\sqrt{2}\ cm$

To find the area of the triangle.

Solution:

The legs of the right triangle means the base and height of the triangle and thus, we can apply the formula to find the area of the triangle.

$Area\ of\ triangle= \frac{1}{2}\times base\times height$

Plugging in base and height of the triangle in the formula.

$Area\ of\ triangle= \frac{1}{2}\times 5\sqrt{2}\times4\sqrt{2}$

$Area\ of\ triangle= \frac{1}{2}\times 20(\sqrt{2})^2$

$Area\ of\ triangle= \frac{1}{2}\times 20(2)$

$Area\ of\ triangle= 20\ cm^2$

Thus, area of triangle = 20 sq. cm.