Question

The legs of a right triangle are in the ratio of 3 to 1. If the length of the hypotenuse of the triangle is 40√40, then the perimeter of the triangle is betweenA. 14 and 15B. 13 and 14C. 12 and 13D. 11 and 12E. 10 and 11

Answer 1

A. Between 14 and 15.

Explanation:

Let x be the one leg of the right triangle.

We have been given that the legs of a right triangle are in the ratio of 3 to 1. So, the other leg of the right triangle would be 3x.

We are also told that the length of the hypotenuse of the triangle is √40.

Using Pythagoras theorem, we can set am equation as:

`x^2+(3x)^2=(√(40))^2`

Let us solve for x.

`x^2+9x^2=40`

`10x^2=40`

`(10x^2)/(10)=(40)/(10)`

`x^2=4`

Take square root of both sides:

`x=√(4)`

`x=2`

The other leg would be
`3x\Rightarrow 3\cdot 2=6`.

The perimeter of the triangle would be:

`\text{Perimeter of triangle}=2+6+√(40)`

`\text{Perimeter of triangle}=2+6+6.324555`

`\text{Perimeter of triangle}=14.324555`

Therefore, the perimeter of the triangle is between 14 and 15 and option A is the correct choice.