# What is the height of x given a 2 dimensional right triangle whose sloping side has a length of 13 and with a base of x + 7?

lemjay | High School Teacher | (Level 2) Senior Educator

Posted on

Since we have a right triangle, apply the Pythagorean formula to solve for x. The formula is:

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

where c is the sloping side or the hypotenuse of the triangle, and a and b are the other two sides of the right triangle which corresponds to the height and the base.

So we have,

`x^2 + (x+7)^2 = 13^2`

`x^2 + (x+7)^2 = 169`

Expand `(x+7)^2` .

`x^2+x^2+14x+49=169`

Then, combine like terms.

`2x^2+14x+49=169`

Express the equation in quadratic form `ax^2+bx+c =0` . So move 169 to the left side.

`2x^2+14x+49-169=0`

`2x^2+14x-120 = 0`

Since 2, 14 and -120 are all divisible by 2, divide both sides by 2.

`(2x^2+14x-120)/2 = 0/2`

`x^2+7x - 60 = 0`

Then, factor left side.

`(x-5)(x+12) = 0`

To solve for x, set each factor equal to zero.

`x-5=0`               and             `x+12=0`

`x=5 `                                        `x=-12`

Since x represent the height of the triangle, consider only the positive value of x.

Hence, the height of the right triangle is 5.

We’ve answered 318,001 questions. We can answer yours, too.