Question

One side of a rectangle is 9 inches shorter than the other side. If the longer side of this rectangle decreases by 5 inches, and the shorter side increases by 3 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle.

Answer 1

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Dimensions of the original rectangle is :

• length = 15 inches

• breadth = 6 inches

Let's assume the dimensions of the rectangle :

$➪breadth = x \: \: inches$

$➪ \: length = (x + 9) \: inches$

Length decreases by 5 inches :

Length now will be :

$→(x + 9)-5 \: inches$

$→x + 9 - 5 \: inches$

$→x + 4 \: inches$

Breadth increases by 3 inches :

Breadth now will be :

$→x + 3 \: inches$

Now, Calculate the dimensions :

Given:-

The area remains same for the original rectangle and the new rectangle.

$Area \: of \: the \: original \: rectangle \: :l \times b$

Where,

• l(lenght )= x+9
• b(breadth)= x

So,the area of the original rectangle is :

$→(x + 9) \times x$

$→ {x}^{2} + 9x$

And also,

Area of the new rectangle is :

$(x + 4)(x + 3)$

$→ {x}^{2} + 3 \times 4 + 4x + 3x$

$→ {x}^{2} + 7x + 12$

According to the QUESTION

$⇒ {x}^{2} + 7x + 12 = {x}^{2} + 9x$

$⇒12 = 9x - 7x$

$⇒9x - 7x = 12$

$⇒2x = 12$

$⇒x = 6 \: inches$

Therefore, the lenght will be

$x + 9 \: inches$

$⇒6 + 9 \: inches$

$⇒15 \: inches$

Answer 2

Step-by-step explanation:

12=9x−7x

⇒9x - 7x = 12⇒9x−7x=12

⇒2x = 12⇒2x=12

⇒x = 6 \: inches⇒x=6inches

Therefore, the lenght will be

x + 9 \: inchesx+9inches

⇒6 + 9 \: inches⇒6+9inches

⇒15 \: inches⇒15inches