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

Answer:

A. Between 14 and 15.

Step-by-step 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:

$x^2+(3x)^2=(\sqrt{40})^2$

Let us solve for x.

$x^2+9x^2=40$

$10x^2=40$

$\frac{10x^2}{10}=\frac{40}{10}$

$x^2=4$

Take square root of both sides:

$x=\sqrt{4}$

$x=2$

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

The perimeter of the triangle would be:

$\text{Perimeter of triangle}=2+6+\sqrt{40}$

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

$\text{Perimeter of triangle}=14.324555$

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