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The length of a rectangle exceeds the width by 5 cm. If both were increased by 3 cm, the area would be increased by 96 cm². Find the dimensions of the original rectangle. [Hint: The original rectangle has area w(w +5).]

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Answer:19cm and 12 cm

Explanation:

Let the length of the rectangle be x and width be y.

From the 1st condition,
The length of a rectangle exceeds the width by 5cm
i.e
x=y+5____(i)

From the 2nd condition,

If both were increased by 3cm the are would be increased by 96cm²
i.e
(x+3)(y+3)=xy+96 (here xy is the original area of the rectangle)
xy+3x+3y+9=xy+96
xy-xy+3x+3y=96-9 (canceling xy)
3(x+y)=87 (taking 3 common)

x+y=87/3 (changing the side of 3)
x+y=29_____(ii)

substituting the value of x in eqn(ii) from eqn(i)
x+y=29
y+5+y=29
2y=29-5
2y=24
y=24/2
y=12cm

Replacing the value of y in eqn(i)

x=y+5
x=12+5
x=19cm

The dimensions of the original rectangle are 19 cm and 12cm


Its my first time answering questions. Hope this helped.

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