Question

The length of a rectangle is 5 cm less than twice the width. The area is 75 square cm.

Find the length and the width.

Answer 1

• L = 10 cm
• W = 7.5 cm

Explanation:

We know that:

• Area = 75 cm²
• LW = 75 cm²
• L = 2W - 5

Work:

• LW = 75
• => (2W - 5)W = 75
• => 2W² - 5W = 75
• => 2W² - 5W - 75 = 0
• => (2W - 15)(W + 5) = 0
• => 2W = 15
• => W = 7.5
• => LW = 75
• => L(7.5) = 75
• => L = 10

Hence, the value of L and W is 10 cm and 7.5 cm respectively.

Answer 2

Area A = LW = 75 cm^2. We also have

L = 2W - 5

Substituting this we have

(2W - 5)W = 75

2W^2 - 5W - 75 = 0

(2W - 15)(W + 5) = 0

so that

2W = 15

W = 7.5 cm and L = 2(7.5) - 5 = 10 cm

hope this helps :)