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Question

The length of a rectangular board exceeds its breadth by 8cm. If the length were decreased by a 4 cm and the breadth doubled. the area of the board would be increased by 256 sq.cm,. Find the length of the board.

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Solution

We have,

Let the length of rectangular board=xcm.

The breadth =ycm.

Now,

According to given question,

length=breadth+8

x=y+8......(1)

Again, according to given question,

(x4)2y=256

(x4)y=128

xy4y=128......(2)

Put the value of x in equation ( 2) and we get,

(y+8)y4y=128

y2+8y4y128=0

y2+4y128=0

Using quadratic formula and we get,

y=4±16+4×1×1282×1

y=4±16+5122

y=4±5282

y=4±5282

y=4±4332

y=2±233

y=2(1±33)

Put the value in equation ( 1) and we get,

x=2(1±33)+8

x=2±233+8

x=6±233

Hence, this is the answer.


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