Question

The length of a hall exceeds its breadth by 12 m. If the perimeter of the hall is 76 m, find the cost of carpeting it at rupees 4 per m square 2​

Answer 1

Step-by-step explanation:

ANSWER

Let x be the breadth of hall. Then, x+8 will be its length.

l=(x+8)m and b=xm

⇒  Area of hall =180m2

⇒  l×b=180

⇒  (x+8)×x=180

⇒  x2+8x−180=0

⇒  x2+18x−10x−180=0

⇒  x(x+18)−10(x+18)=0

⇒  (x+18)(x−10)=0

∴  x=10

l=x+8=10+8=18m and b=10m

⇒  Perimeter of hall =2(l+b)

                                   =2(18+10)

                                   =2(28)

                                   =56m

Answer 2

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Let breadth be x

Length=x+12

Perimeter=76

Perimeter=2×(l+b)

76=2×(x+x+12)

76=2×(2x+12)

76=4x+24

76-24=2x

52=2x

$\sf \frac{52}{2} = x = 26$

So breadth=26 m

Length= 26+12=38 m

Area=l×b

26×38=988 m²

Cost of carpenting 1m²=₹4

Cost of carpenting the hall = 988× 4 = ₹3952

So the cost of carpenting the hall is ₹3952

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