Question

9. The length of a rectangle is 2p cm and its breadth is p cm. When the length of the rectangle is increased by 25% and the breadth is decreased by 25%, determine the percentage change in (i) its perimeter, (ii) its area. ​

Answer 1

i = 8 1/3%

ii = -6 1/4%

Explanation:

The previous answer is wrong this is the correct one:

Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm

i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm

The percentage change is

65-60/60 x 100

= 5/60 x 100

= 500/60

= 8 2/6% simplified 8 1/3%

ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2

The percentage change is

187,5-200/200x 100

= - 12,5/200 x 100

= - 1250/200 = - 6 1/4 %

That is the Correct answer. Hope that help

Answer 2

The answers are:
(i) 108.33%
(ii) 93.75%

Explanation:

The original area and perimeter are as follow:

Perimeter = 2l + 2w
= 2(2p) + 2(p)
= 4p + 2p
= 6p cm

Area = l * w
= 2p * p
= 2p^2 cm^2

A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm

A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm

Perimeter = 2l + 2w
= 2(2.5p) + 2(0.75p)
= 5p + 1.5p
= 6.5p cm

Area = l * w
= 2.5p * 0.75p
= 1.875p^2 cm^2

Now that we have found the changes, let's calculate the percentage changes

Percentage change of perimeter:

x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33

Percentage change of area:

x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75