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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
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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