Answer:
Length = 5 cm, width = 2 cm.
Step-by-step 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.
