Question

Perimeter of a rectangular concrete slab is 102 feet and it's area is 560 ft.² what is the length of the longer side of the slab

Answer 1

The longer length is 35ft

Explanation:

Given

`Area = 560`

`Perimeter = 102`

Required

Determine the longer length

Represent the length with L and width with W

So, we have:

`L * W = 560` --- Area

`2*(L+W) = 102` --- Perimeter

Divide both sides by 2 in:

`2*(L+W) = 102`

`L + W = 51`

Make L the subject:

`L = 51 - W`

Substitute 51 - W for L in
`L * W = 560`

`(51 - W) * W = 560`

`51W - W^2 = 560`

Reorder the equation

`W^2 - 51W + 560 = 0`

Expand

`W^2 -35W - 16W + 560 = 0`

`W(W-35)-16(W-35) = 0`

`(W-16)(W-35) = 0`

Split:

`W - 16 = 0\ \ \ W - 35 = 0`

`W = 16\ \ \ W = 35`

This implies that the longer length is 35ft