Question

The perimeter of a rectangle is 30 cm. If one of its sides is decreased by 3 cm and the other side is increased by 5 cm, the area of the rectangle will decrease by 8 cm^2. Find the area of the original rectangle.

Answer 1

Answer:

I think your qs is wrong

Step-by-step explanation:

Let the length be x cm and breadth be y cm.

Now, 2(x + y) = 30 =》 x + y = 15

=》 y = 15 - x --- i

A/Q, (x + 5)(y - 3) = xy - 8

= x(y - 3) + 5(y - 3) = xy - 8

= xy - 3x + 5y - 15 = xy - 8

= 5y - 3x = 15 - 8 =》 5y - 3x = 7

= 5(15 - x) - 3x = 7 =》 75 - 5x - 3x = 7

= 8x = 68 =》 x = 17/2 =》 x = 8.5 cm

Putting this value in i

= y = 15 - 8.5 =》 y = 6.5 cm

Answer 2

Step-by-step explanation:

Formula:

Perimeter of a Rectangle =2(length x Breadth)

length = l

breath =b

Given: Perimeter of a rectangle =30cm

using formula:

Perimeter of a rectangle = 2(lxb) sq units

=> 30 = 2(lxb)

=> 30/2 = lxb

=> 15 = lxb

i.e b = 15-l (equation (1))

Now, using formula: Area of a rectangle = lxb sq.units

Given: Area of a rectangle is decreased by 8.

length is decreased by 3 and

Breadth is increased by 5.

lets us write it as Area = (a-8), length = l-3, Breadth = b+5.

Using formula:

Area of a rectangle = lxb sq units

=> a-8 = (l-3) x (b+5)

=> (lxb) -8 = (l-3) x (b+5) {a is area so write it as lxb}

=> lb - 8 = lb + 5l - 3b - 15 [multiplied]

=> - 8 = 5l -3b -15 [both side lb cancelled]

=> 15 - 8 = 5l - 3b

Using equation (1); b= 15-l

=> 15 - 8 = 5l - 3b

=> 7 = 5l - 3(15 - l)

=> 7 = 5l - 45 + 3l

=> 45 + 7 = 5l + 3l

=> 52 = 8l

=> 8l = 52

=> l = 52/8

=> length(l) = 6.5 cm

Again Using equation (1); b = 15- l

=> b = 15 - 6.5 (length (l) = 6.5cm)

=> b = 8.5 cm

Therefore, area of the original Rectangle = l x b sq units

= 6.5 x 8.5

= 55.25 cm^2

Note:

Area of a rectangle = (l-3) x (w+5) = 3.5 x 13.5 = 47.25 cm^2

The difference = Area of the original Rectangle - Area of a rectangle

= 55.25 - 47.25

= 8cm^2

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