Question

The length of a rectangle is $\frac{3x}{4}+1$ and its breadth is $\frac{2x}{3}-1$. If its perimeter is $34$ units. Find $x.$

Answer 1

Given: Length of rectangle, $l=\frac{3x}{4}+1$

Breadth of rectangle, $b=\frac{2x}{3}-1$

Perimeter of the given rectangle $=34$ units.

We know that the Perimeter of rectangle is given by $2(l+b)$

$\Rightarrow 2[\frac{3x}{4}+1+\frac{2x}{3}-1]=34$

$\Rightarrow 2\left[\frac{3x\times 3+2x\times 4}{4\times 3}\right]=34$

$\Rightarrow \left[\frac{9x+8x}{2\times 3}\right]=34$

$\Rightarrow \frac{17x}{6}=34$

$\Rightarrow x=\frac{34\times 6}{17}$

$\therefore x=12$