Question

the sum of legs for a right triangle be 21 and their product is 40. Find the perimeter of this triangle.​

Answer 1

The perimeter of the triangle is 40.

Explanation:

The sum of legs for a right triangle is 12:

`a + b = 21`

`a = 21 - b` (1)

And their product is:

`a*b = 40` (2)

By entering eq (1) into (2) we have:

`(21 - b)b = 40`

`21b - b^(2) - 40 = 0`

We can find the value of "b" by solving the above quadratic equation.

`b_(1) = 2.1`

`b_(2) = 18.9`

Since the two values satisfy the equation, we can use either of them to find "a". We will use b₁.

`a = 21 - 2.1 = 18.9`

Now, the hypotenuse of the right triangle is given by:

`h = \sqrt{a^(2) + b^(2)} = \sqrt{(18.9)^(2) + (2.1)^(2)} = 19`

Hence, the perimeter is:

`P = a + b + h = 18.9 + 2.1 + 19 = 40`

Therefore, the perimeter of the triangle is 40.

I hope it helps you!