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

Answer:

The longer length is 35ft

Step-by-step 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