Question

The hypotenuse of a right triangle is three times the length of its first leg. The length of the other leg is four feet. Find the lengths of the first leg and the hypotenuse and enter them in the below spaces in this order. For non-integer answer(s), round your answer(s) to the nearest tenth.

Answer 1

The length of hypotenuse is 4.2 feet and length of first leg is 1.4 feet.

Explanation:

Consider the provided information.

Let x is the length of the first leg.

It is given that the hypotenuse of a right triangle is three times the length of its first leg.

Hypotenuse = 3x

The length of the other leg is 4 feet.

Pythagorean theorem.

`a^2+b^2=c^2`

Where a and b are the legs and c is the hypotenuse.

Substitute the respective values in the above formula.

`x^2+4^2=(3x)^2`

`x^2+16=9x^2`

`16=8x^2`

`2=x^2`

`√(2)=x`

x = 1.4 feet(nearest tenth)

The length of hypotenuse = 3x = 3×1.4 = 4.2 feet

The length of hypotenuse is 4.2 feet and length of first leg is 1.4 feet.