Question

The length of a rectangle is $6$ m less than three times its breadth. The length and breadth of the rectangle, if its perimeter is $148$ m, is ___________.

• A. $54$ m, $20$ m
• B. $50$ m, $30 m
• C. $40$ m, $25$ m
• D. $30$ m, $20$ m

Answer 1

Answer: (A)

$54$ m, $20$ m

Let the length and breadth of rectangle be l and b .

Given that length is $6$m less than three times its breadth

$\Rightarrow l=3b-6$.............................(i)

Given its perimeter is $148$m.

we k.n.t perimeter of a rectangle is $2(l+b)$

$\Rightarrow 2(l+b)=148$

$\Rightarrow (l+b)=\frac{148}{2}=74$.........(ii)

Substitute (i) in (ii)

$l+b=(3b-6)+b=74$

$4b=74+6=80$

$b=\frac{80}{4}=20$

Substituting value of b in (i)

$l=3b-6=3\left(20\right)-6=60-6=54$

Thus,length and breadth of given rectangle are $54m,20m$.