Question

The length of a verandah is 3 m more than its breadth The numerical values
of its area is equal to the numerical value of its perimeter
Taking as the breadth of the verandah, write an equation in that
represents the above statement.
​

Answer 1

Let breadth = xm, length = (x + 3)m.

Area = x(x + 3) sq. m.

Perimeter = 2(x + x + 3) = (4x + 6)m.

According to the question, x(x+ 3) = 4x + 6

⇒ x2 – x – 6 = 0

⇒ (x + 2) (x – 3) = 0

∴ x = 3 and x = - 2 (inadmissiable).

Hence breadth = 3m, length = 6m.

Answer 2

let the lenghth be xm and breadth be ym.

A/Q:x=y+3

area = xy

= (y+3)y=y^+3y sq.m

perimeter= 2(x+y)

=2(y+3+y)=2(2y+3)

=4y+6 m

y^+3y=4y+6

y^-y-6=0

y^-3y+2y-6=0

y(y-3)+2(y-3)=0

(y+2)(y-3)=0

so,y=-2 and y=3

y cant be negative . so, breadth=3m and length=y+3=6m

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