Question

Length of a rectangle is 7 m less than four times its breadth. If the perimeter of the rectangle is 56 m, then find its length and breadth.

• A. 21 m and 7 m
• B. 25 m and 8 m
• C. 17 m and 6 m
• D. 13 m and 5 m

Answer 1

The correct option is A 21 m and 7 m

Let the breadth of the rectangle be $x$ m.
Then according to the given data, the length of the rectangle is $(4x-7)$ m.

Perimeter of a rectangle $=2\times (length+breadth)$

Therefore,
$2\times \left(\right(4x-7)+x)=56$
$2\times (5x-7)=56$
$10x-14=56$
$10x=56+14$
$10x=70$
$x=\frac{70}{10}$
$x=7$

So, the breadth of the rectangle = 7 m.
Length of the rectangle $=4x-7=(4\times 7)-7=28-7=21m$