A rectangle has an area of 30 square meters and a perimeter of 34 meters what are the dimensions of the rectangle

Answer 1

Area = length x width

Let L be length and w be width

LW=30

Divide by w so L=30/w

Perimeter is all the sides added together. There are 2 lengths and 2 widths so the equation could be

P=2L+2W=34

Substitute L=30/w

2(30/w)+2w=34

60/w+2w=34

Multiply both sides by w

60+2w²=34w

Subtract 34w from both sides

2w²-34w+60=0

Factor out a 2

2(w²-17w+30)=0

Factor

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

Set each equal to zero

w-2=0 so w=2

w-15=0 so w=15

Since L=30/w

When w=2 L=15

When w=15 L=2

Usually the length is a bigger side than width so

Length is 15 meters and the width is 2 meters