Question

- One leg of a right triangle is 4 inches longer than the other leg. The hypotenuse is 20 inches long. What is thelength of the shortest side?

Answer 1

Let's name the a, b, c

let side a = x

let side b = 4+x

Let side c = hypotenuse = 20

Using the law of pythagoras

opposite² + adjacent² = hypotenus²

x² + (x+4)² = 20²

open the parenthesis

x² + x² + 4x +16 = 400

2x² + 4x + 16 = 400

2x² + 4x + 16 - 400 = 0

2x² + 4x - 384 = 0 --------------------------------(1)

The is now a quadratic equation

so we will solve and find x

Using the formula method

Quadratic formula is

`x\text{ = }(-b\pm√(b^2-4ac))/(2a)`

Comparing equation (1) with ax² + bx + c = 0

a = 2 b = 4 and c= -384

Inserting the values into the formula

`x\text{ = }\frac{-4\text{ }\pm\sqrt{4^2\text{ - 4(2)(-384)}}}{2(2)}`

simplifying the above

`x\text{ = }\frac{-4\pm\sqrt{16\text{ + 3072}}}{4}`