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Elena L [17]
2 years ago
6

Please help me solve this :)

Mathematics
1 answer:
DENIUS [597]2 years ago
6 0
1/4,1/2,1/2,5/4,0,0,1,1,1,2,2
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Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what coul
aev [14]

The length of the rug is 4 ft.

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Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

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Thus, the length of the rug is l=1.5+w

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

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10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0

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Substituting the values, we have,

$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\

$w=\frac{-15 \pm \sqrt{4225}}{20}$

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Thus,

w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5  and   w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting w=2.5 in l=1.5+w, we get,

l=1.5+2.5\\l=4

Thus, the length of the rug is 4 ft.

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