Question

In a square if length and breadth are increased and decreased respectively by $7$ units to form a rectangle, the ratio of original area to that after changes are made is $4:3$. Find the measure of length and breadth of rectangle formed.

• A. length$=14$units
  breadth$=7$ units
• B. Length $=21$units
  Breadth$=7$units
• C. Length $=7$units
  Breadth$=21$units
• D. Length $=21$units
  Breadth$=14$units

Answer 1

The correct option is B Length $=21$units

Breadth$=7$units
Let the side of square be $a$units.

Area of square will be $=a\times a=a^2$

Now, length is increased by $7$ units
$\Rightarrow$ length$=a+7$units

And, breadth is decreased by $7$units
$\Rightarrow$ breadth$=a-7$units

New area of rectangle formed will be $=(a-7)(a+7)$
$\Rightarrow$ area $=a^2-7^2=a^2-49$

According to question
$\frac{a^2}{a^2-49}=\frac{4}{3}$

On simplifying we get,
$\Rightarrow 3a^2=4(a^2-49)$

$\Rightarrow 3a^2=4a^2-49\times 4$

$\Rightarrow 49\times 4=4a^2-3a^2$

$\Rightarrow 196=a^2$

$\Rightarrow a=14$units

Now Length and breadth of rectangle formed will be $(14+7)=21$units and $(14-7)=7$units respectively.