U2.L5.HW: Quadratic Equations: Question 38

Question

One side of a rectangle is twelve miles longer than three times another side of the rectangle. Find the sides if we also know that the area of the rectangle is 231 mi².

shorter side: __________ mi

longer side: _____________mi

Answer 1

Hi Manny Y

Shorter side 7 mi

Longer side 33 mi

Area of a Rectangle = Length times Width or just l*w

l*w = 231mi²

Let the shorter side = w

According the information above, the longer side = l = 3w + 12

w(3w + 12) = 231

3w² + 12w = 231

If we subtract 231 from both sides of the equation we have the following quadratic

3w² + 12w - 231 = 0

factor the quadratic

(3w - 21)(w + 11) =0

Length cannot be negative

3w - 21 = 0 is the only useful factor

3w = 21

w = 7 mi

l = 3w + 12 = 21 + 12 = 33 mi

Checking

7mi * 33mi = 231mi²

Answer 2

231 = s(3s + 12)

231 = s² + 12s

0 = s² + 12s - 231

Can you factor, solve, and answer?