Answered

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Lowe sold a square carpet,and also a rectangular carpet whose length was 5/4 the width.The combined area of the two was 405 ft square.The price of the first carpet $10 per square yard ,and of the second $12 per square yard.If $10 more was received for the square piece than the other ,find the dimension of each

Sagot :

Jers15idn
Price of carpet:
Price of carpet:
Square=$10 per yd²
Rectangle=$12 yd²

The square:
A1=Area of the square
L1=length of the side of the square
A1=L²

The rectangle:
A2=Area of the rectanble
L=length of the rectangle
W=width of the rectangle
A2=LW


The length was 5/4 the width
[tex]L=\frac{5}{4}(w)[/tex]
or simply:
[tex]W=\frac{4}{5}(L)[/tex]

The Combined Area of the two was 405 ft²
A1+A2=405ft²
L²+LW=405ft²
L²+[tex]\frac{4}{5}L^2[/tex]=405ft²
[tex]\frac{9L^2}{5}[/tex]=405ft²
Multiply both sides by 5
9L²=2025
Divide both sides by 9
L²=225ft²
Square root both sides
L=15ft

Now find the width of the rectangle:
L=[tex]\frac{5}{4}W[/tex]
15ft=[tex]\frac{5}{4}W[/tex]
Multiply both sides by 4
60ft=5W
Divide both sides by 5
W=12ft

Now find the area of the rectangle:
A2=LW
A2=15ft(12ft)
A2=180ft²

Substitute to the equation to find the area of the square
A1+A2=405ft²
A1+180ft²=405ft²
Subtract both sides by 180ft²
A1=225ft²
Now substitute the value of A1
L²=225ft²
Square root both sides
L=15ft

I don't think the price is useful for this question. But hope this helps =)


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