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

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

B. 20 sq. cm

Explanation:

Given:

The legs of a right triangle measure:

`5√(2)\ cm` and
`4√(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= (1)/(2)* base* height`

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

`Area\ of\ triangle= (1)/(2)* 5√(2)*4√(2)`

`Area\ of\ triangle= (1)/(2)* 20(√(2))^2`

`Area\ of\ triangle= (1)/(2)* 20(2)`

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

Thus, area of triangle = 20 sq. cm.