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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

Sagot :

MrRoyalidn

Answer:

The longer length is 35ft

Step-by-step explanation:

Given

[tex]Area = 560[/tex]

[tex]Perimeter = 102[/tex]

Required

Determine the longer length

Represent the length with L and width with W

So, we have:

[tex]L * W = 560[/tex] --- Area

[tex]2*(L+W) = 102[/tex] --- Perimeter

Divide both sides by 2 in:

[tex]2*(L+W) = 102[/tex]

[tex]L + W = 51[/tex]

Make L the subject:

[tex]L = 51 - W[/tex]

Substitute 51 - W for L in [tex]L * W = 560[/tex]

[tex](51 - W) * W = 560[/tex]

[tex]51W - W^2 = 560[/tex]

Reorder the equation

[tex]W^2 - 51W + 560 = 0[/tex]

Expand

[tex]W^2 -35W - 16W + 560 = 0[/tex]

[tex]W(W-35)-16(W-35) = 0[/tex]

[tex](W-16)(W-35) = 0[/tex]

Split:

[tex]W - 16 = 0\ \ \ W - 35 = 0[/tex]

[tex]W = 16\ \ \ W = 35[/tex]

This implies that the longer length is 35ft

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