Question

What is the remaining leg of a right triangle if the hypotenuse is 13 units and the other leg is 4 units?

Answer 1

Other side = 2 or

Explanation:

Given : The leg of a right triangle is 2 units and the hypotenuse is 4 units.

To find : What is the length, in units, of the other leg of the triangle.

Solution : We have given

Leg of a right triangle = 2 units.

Hypotenuse = 4 units.

By the Pythagorean theorem :

(Hypotenuse)² = (One leg)² + (other leg)².

Plug the values,

(4)² = (2)² + (other leg)².

16 = 4 + (other leg)².

On subtracting both sides by 4

16 - 4 = (other leg)².

12 = (other leg)².

Taking square root.

Other side = 2 .

Therefore, Other side = 2 or

Answer 2

The hypotenuse of a right triangle is 13 units. If the length of one leg is 2 more than twice the other, then what are their lengths?

Let x = one leg

then

2x+2 = other leg

.

applying Pythagorean theorem:

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

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

x^2 + 4x^2+8x+4 = 169

5x^2+8x+4 = 169

5x^2-25x+33x-165 = 0

(5x^2-25x)+(33x-165) = 0

5x(x-5)+33(x-5) = 0

(x-5)(5x+33) = 0

x = {-33/5, 5}

Throw out negative solution (extraneous) leaving:

x = 5 units (one leg)

.

other leg:

2x+2 = 2(5)+2 = 10+2 = 12 units