Question

The length of a rectangle exceeds its breadth by $9$ cm. If the length and breadth are each increased by $3$ cm, then the area of the new rectangle will be $84{cm}^2$ more than that of the given rectangle. Find the length and breadth of the given rectangle.

• A. Breadth of the rectangle is $13$ cm and length $=29$ cm
• B. Breadth of the rectangle is $5$ cm and length $=14$ cm
• C. Breadth of the rectangle is $3$ cm and length $=10$ cm
• D. Breadth of the rectangle is $8$ cm and length $=17$ cm

Answer 1

Answer: (D)

Breadth of the rectangle is $8$ cm and length $=17$ cm

Let the breadth of the rectangle be $x$ cm.

Then, the length of the rectangle is $(x+9)$ cm.
So, area of rectangle $=$ length $x$ breadth $=x(x+9){cm}^2$
Now, length of new rectangle $=(x+9+3)$ cm $=(x+12)$ cm and
breadth of new rectangle $=(x+3)$ cm.
So, area of new rectangle $=$ length $\times$ breadth $=(x+12)(x+3){cm}^2$

According to the given condition,
$(x+12)(x+3)=x(x+9)+84$

$\Rightarrow x^2+12x+3x+36=x^2+9x+84$

$\Rightarrow 15x+36=9x+84$

$\Rightarrow 15x-9x=84-36$

$\Rightarrow 6x=48\Rightarrow x=8$

$\text{So, breadth of the rectangle is}$ $8$ $\text{cm and length}$

$=8+9=17$ $cm$.