Question

the length of a rectangular floor is 3 more than its breadth. if the numerical values of its area and perimeter are equal then form an equation for breath x . also find the dimensions of the floor.​

Answer 1

Solution-

Let the breadth of the rectangular floor be l cm.

A/q, length of the rectangular floor = (x+3)cm.

Given, Area (floor) = Perimeter (floor)

(x+3)x = 2[(x+3)+x]

x² + 3x = 2[2x+3]

x² + 3x = 4x + 6

x² - x - 6 = 0

x² - 2x + 3x - 6 = 0. (on factorizing)

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

(x+3) = 0 | (x-2) = 0

x= -3 | x= 2

Hence, Breadth = x cm = 2 cm

⇒ Length = (x+3)cm = (2+3)cm = 5 cm.

Dimensions of the rectangular floor

= l×b = (5×2) cm.

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Answer 2

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If breadth=x,

then length=x+3

Given

Area & perimeter are same

so,x(x+3)=2[x+(x+3)],

x^2+3x=4x+6

x^2-x-6=0

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

x(x-3)-2(x-3)=0

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

x=3 or x =-2

x=3,

so,length=3+3=6

Breadth= 3

Length = 3+3=6

Hence ,the dimensions of the floor is 3 and 6.