Question

The length of a rectangle exceeds the breadth by 5 cm. If the length is decreased by
I cm and the breadth is increased by 3 cm, then the area of the new rectangle increases
by 32 cm. Find the dimensions of the original rectangle.
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Answer 1

Step-by-step explanation:

solution -

let the breadth of the rectangle =x cm.

the length = (x +5)cm

area = x ( x+5)cm^2= (x^2+5)cm^2

new length = {(x+5)-1}=(x+4)cm

new breadth =(x+3)cm

area of the new rectangle = (x+4) (x+3)cm^2

=( x^2+7x+12)cm^2

according to the question,

area of new rectangle - area of given rectangle=32

=( x^2+7x+12) - (x^2+5x)=32

=x^2+7x+12-x^2-5x = 32

=2x+12 =32

2x= 20

x=10

therefore the breadth of the given reactangle is 10 cm and its lenght is 15 cm.

Answer 2

$hello$

Let the original length and breadth be l and b.

l = x

b = x + 5.

Now,

New length, l = x - 1

New length, l = x - 1New breadth, b = x + 8.

Area of the new triangle exceeds the area of the original triangle.

(x - 1)(x + 8) = x(x + 5) + 32

x² + 8x - x - 8 = x² + 5x + 32

8x - x - 5x = 32 + 8

2x = 40

x = 20 cm.

So, the length and breadth of the rectangle is 25 cm and 20 cm, respectively.

I hope my answer helps you....✌