Question

Here is a rectangle ABCD.

A B
20cm

C D
30cm

The length of the rectangle is increased by 10%.
The width of the rectangle is increased by 5%.

Find the percentage increased in the perimeter of the rectangle

Answer 1

8%

Explanation:

Answer 2

8%

Explanation:

Original perimeter is 100cm

• The 20cm is representative of the width
• 30cm is representative of the length

length is increased by 10%

• 30+(.10 x 30)
• (1 + .10) × 30
• (100% + 10%) × 30
• 110% × 30
• 110 ÷ 100 × 30
• 110 × 30 ÷ 100
• 3,300 ÷ 100
• = 33

length is increased by 5%

• 20 + (5% × 20) =
• 20 + 5% × 20 =
• (1 + 5%) × 20 =
• (100% + 5%) × 20 =
• 105% × 20 =
• 105 ÷ 100 × 20 =
• 105 × 20 ÷ 100 =
• 2,100 ÷ 100 =
• = 21

New perimeter: 108 cm

Percentage increase:

• (108-100):100*100 =
• (108:100-1)*100 =
• 108-100 = 8
• = 8%

Hopefully this helps