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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
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B
50 m, $30 m
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C
40 m, 25 m
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D
30 m, 20 m
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Solution

The correct option is C $$54$$ 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 $$2(l+b)$$
$$\Rightarrow 2(l+b)=148$$
$$\Rightarrow (l+b)=\dfrac{148}{2}=74$$.........(ii)

Substitute (i) in (ii)
$$l+b=(3b-6)+b=74$$
$$4b=74+6=80$$
$$b=\dfrac{80}{4}=20$$
Substituting value of b in (i)
$$l=3b-6=3(20)-6=60-6=54$$

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

Mathematics

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