SOLUTION: the length of a rectangular board is 9 inches more than its width, the area is 112 square inches. Find the measures of the length and the width Please help me😭😭&

Algebra ->  Rectangles -> SOLUTION: the length of a rectangular board is 9 inches more than its width, the area is 112 square inches. Find the measures of the length and the width Please help me😭😭&      Log On


   

Question 1086553: the length of a rectangular board is 9 inches more than its width, the area is 112 square inches. Find the measures of the length and the width
Please help me😭😭😭
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
L = length (in inches)
W = width (in inches)

We're given that the "the length...is 9 inches more than its width", so

L+=+W%2B9

The area of any rectangle is found by the formula

A+=+L%2AW

Make substitutions and get everything to one side

A+=+%28W%2B9%29%2AW Replaced L with W+9

112+=+%28W%2B9%29%2AW Replaced A with 112

112+=+W%2AW+%2B+9%2AW

112+=+W%5E2+%2B+9W

112-112+=+W%5E2+%2B+9W+-+112

0+=+W%5E2+%2B+9W+-+112

W%5E2+%2B+9W+-+112+=+0

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From here use the quadratic formula. It is the most effecient way to solve quadratic equations.

Using the quadratic formula, we get

W+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

W+=+%28-%289%29%2B-sqrt%28%289%29%5E2-4%281%29%28-112%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+9, c+=+-112

W+=+%28-9%2B-sqrt%2881-%28-448%29%29%29%2F%282%29

W+=+%28-9%2B-sqrt%2881%2B448%29%29%2F%282%29

W+=+%28-9%2B-sqrt%28529%29%29%2F2

W+=+%28-9%2Bsqrt%28529%29%29%2F2 or W+=+%28-9-sqrt%28529%29%29%2F2

W+=+%28-9%2B23%29%2F2 or W+=+%28-9-23%29%2F2

W+=+14%2F2 or W+=+-32%2F2

W+=+7 or W+=+-16

Ignore the value W+=+-16. It's not possible to have a negative width.

The only practical solution is W+=+7

If the width is W+=+7, then the length L is

L+=+W%2B9

L+=+7%2B9

L+=+16

Note how L*W = 7*16 = 112 so that helps confirm the answers.

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Answers:
Length = 16 inches
Width = 7 inches

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

the length of a rectangular board is 9 inches more than its width, the area is 112 square inches. Find the measures of the length and the width
Please help me😭😭😭
ALL you need to do is find two FACTORS of 112 that DIFFER by 9. Those will be your length and width measurements.

That's all....nothing COMPLEX and/or CONFUSING!!