Mathematics: Acarpenter 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

Acarpenter is assigned the job of expanding a

sam10146

12.03.2022

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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