Question

The Perimeter of the quadrilateral is 30 centimeters. Find the length of each side. The sides are: x+5, x+3, 2x-2, x^2-2x

Answer 1

9 cm, 7 cm, 6 cm and 8 cm

Explanation:

The perimeter is the sum of all the sides.

4 sides' expressions are given, so we add them and equate to 30.

`x+5+x+3+2x-2+x^2-2x=30\\x^2+2x+6=30\\x^2+2x+6-30=0\\x^2+2x-24=0\\(x+6)(x-4)=0\\x=-6,4`

Note: we disregard the value of x = -6, because it is going to give us side with negative length, that can't happen!

So, we take x = 4

Hence, length of each side is:

x + 5 = 4 + 5 = 9 cm

x + 3 = 4 + 3 = 7 cm

2x -2 = 2(4) - 2 = 8 - 2 = 6 cm

x^2 - 2x = (4)^2 - 2(4) = 16 - 8 = 8 cm

These are the lengths of 4 sides: 9 cm, 7 cm, 6 cm and 8 cm.