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yanalaym [24]
3 years ago
5

A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. the length of the deck

is to be expanded by 10 feet, and the width by 6 feet. if the area of the new rectangular deck is 128 ft2 larger than the area of the original deck, find the dimensions of the original deck
Mathematics
1 answer:
anzhelika [568]3 years ago
8 0

Alright, lets get started.

Suppose the original deck size: width = x feet

the width is one-fourth the length given in question means length = 4 x feet

Means the originally area = x * 4 x = 4 x^{2}

Now the dimensions are changed.

New dimensions, width = (x + 6)

new length = (4x+10)

So, new area will be = (x+6) * (4x+10) = 4x^{2} + 10 x + 24 x + 60 = 4x^{2} + 34 x + 60

the area of the new rectangular deck is 128 ft2 larger than the area of the original deck, means

4x^{2} + 128= 4x^{2} + 34 x + 60

Subtracting 4x^{2} from both sides

128 = 34 x + 60

Subtracting 60 from both sides

128 - 60 = 34 x + 60 - 60

68 = 34  x

Dividing 34 in both sides

\frac{68}{34}  = \frac{34 x }{34}

x = 2

Means width = 2 feet

Length would be = 4 time width = 4 * 2 = 8 feet

Means dimension of original deck would be = 2 feet and 8 feet :Answer

Hope it will help :)

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