Question

The length of a rectangle exceeds the breadth by 5cm. If the length is decreased by 1cm and the breadth is increased by 3cm, then the area of the new rectangle increases by 32cm^2. Find the dimensions of the original rectangle.

Thanks!!

Answer 1

Let the original length and breadth be l and b.

l = x

b = x + 5.

Now,

New length, l = x - 1
New 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.

-WonderGirl

Answer 2

Answer: The answer is L=15cm,B=10cm

Step-by-step explanation: Given,

According to the question,

breadth of the original rectangle = x

According to the question length exceeds by 5,

Length of the original rectangle = x+5

And length of the new triangle decreased by 1,

length of the new rectangle = x+5-1

                                               =x+4

Breadth of new rectangle = x+3

Area of new rectangle increased by 32 sp. cm

Area of old rectangle=Area of new rectangle

$(x+4)(x+3)=x(x+5)+32$

multiplying both the brackets,

$x^{2} +4x+3x+12=x^{2} +5x+32$

solving the equation, adding x values and others

$7x+12=5x+32$

transfer the x values in LHS and numeric values on RHS

$7x-5x=32-12$

$2x=20$

divide both the side by 2

$x=10$

Original length of the original rectangle =x+5= 15cm

            Breadthof the original rectangle =x=10cm

#SPJ5

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