Question

The length of a rectangle is 6m less than three times its breadth. Find

the dimensions of the rectangle if its perimeter is 148m.​

Answer 1

Answer:

• Length = 54m
• Breadth = 20m

Explanation:

In a rectangle, the length is 6m less than three times its breadth. And its perimeter is 148m

Let's say that, the breadth of the rectangle is $\boldsymbol{x}$ m

Then, the length will be $\boldsymbol{(3x - 6)}$ m

We know that,

Perimeter of a rectangle = 2(l + b)

Where,

• ‘l’ is the length
• And ‘b’ denotes the breadth.

Substituting the values,

$\sf\implies 148 = 2({\boldsymbol{x}} + 3{\boldsymbol{x} - 6})$

$\sf \implies \: 148 = 2(4{\boldsymbol{x} - 6})$

$\sf \implies \dfrac{148}{2} = 4{\boldsymbol{x}} - 6$

$\sf \implies \: 74 = 4{\boldsymbol{x}} - 6$

$\sf \implies \: 74 + 6 = 4{\boldsymbol{x}}$

$\sf \implies \:80 = 4 {\boldsymbol{x}}$

$\sf \implies{\boldsymbol{x}} = 20$

Hence, the dimensions are :-

• Length = $3{\boldsymbol{x} - 6}$ = 54
• Breadth = ${\boldsymbol{x}}$ = 20