Question

Fifth grade

EE. 12 Area and perimeter: word problems
A rectangular sticker has an area of 10 square centimeters and a perimeter of 14
centimeters. What are the dimensions of the sticker?​

Answer 1

Length = 5 cm, width = 2 cm.

Explanation:

If L is the length and W the width we have the equations:

LW = 10 <----- The area.

2L + 2W = 14 <------ The perimeter.

From the first equation L = 10/W so substituting for L in the second equation:

2 * 10/W + 2W = 14

20/W + 2W = 14 Multiplying through by W:

20 + 2W^2 = 14W

2W^2 - 14W + 20 = 0 Dividing by 2:

W^2 - 7W + 10 = 0

(W - 5)(W - 2) = 0

W = 5 or 2.

So W is either 2 or 5 cm.

Substituting W = 2 in LW = 10

L * 2 = 10

L = 5 cm.

The length is longer than the width so the length is 5 cm and the width = 2 cm.