The longer leg of a right triangle is 7 cm longer than the shorter leg. The hypotenuse is 8 cm longer than the shorter leg. What is the perimeter of the triangle?

Answer 1

Hi Wrestler. The best way to handle a right triangle question, when you receive information about sides, is to know right triangle combinations.

You can start with the 3, 4, 5 right triangle, where 3 and 4 are the shorter sides, and the hypotenuse, 5, is the longest side. The next one would be the 5, 12, and 13. This works, because 12 is 7 more than 5, and 13 is 8 more than 5.

Add 5+12+13, and the perimeter is 30, your answer.

Please consider hiring me as a tutor. Thanks.

Answer 2

Hi there,

First you can write three expressions to represent the legs and the hypotenuse of the triangle.

Using the variable x to represent the shorter leg, we write the following expression for the longer leg: x + 7

The hypotenuse would be represented by the following expression: x + 8

Now use the Pythagorean Theorem to determine the value of x so that you can add all three sides and find the perimeter:

a² + b² = c²

For this triangle:

x² + (x+7)² = (x + 8)²

We can expand this equation and complete the square to find x as follows:

x² + (x+7)² = (x + 8)²

x² + x² + 14x + 49 = x² + 16x + 64

2x² + 14x + 49 = x² + 16x + 64

2x² + 14x + 49 - x² = x² + 16x + 64 - x²

x² + 14x + 49 = 16x + 64

x² + 14x + 49 -16x = 16x + 64 - 16x

x² - 2x + 49 - 49 = 64 - 49

x² - 2x = 15 (Now divide -2 by 2 , square your result and add to both sides)

x² - 2x + 1 = 15 + 1

(x - 1)² =16

x - 1 = 4

x = 5 (Using only positive root)

Since x = 5, the short leg will be 5 cm, the long leg will be 12 cm, and the hypotenuse will be 13 cm.

The perimeter will be 5 + 12 + 13 = 30 cm

Let me know if you have other questions or would like to schedule an online session/lesson.

Take care,

Mrs. R.

Answer 3

x^2 + (x+7)^2 = (x+8)^2

x^2 + x^2 + 14x + 49 = x^2 + 16x + 64

2x^2 + 14x + 49 = x^2 + 16x + 64

x^2 - 2x - 15 = 0

( x - 5 )(x + 3 ) = 0

x+3=0 results in negative measures

x-5=0 -->x = 5

shortest side = 5

longer side = 12

hypotenuse = 13