completing the square

Question

The length of a rectangle is 10 meters more than twice the width. The area of the rectangle is 300m². Find the length and width of the rectangle

Answer 1

Let L be length and w be width

L= 10 +2w

W

Area = L W=300

W(10+2w)=300

Distribute

2w^2+10w=300

Subtract 300 both sides

2w^2+10w-300=0

Factor out a 2

2(w^2+5w-150)=0

Factor

2(w+15)(w-10)=0

W-10=0

W =10

L=10+2(10)=30