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A rectangle with a perimeter of 80 cm has its sides in the ratio 3: 5. What is the area of a square whose side is equal to the length of the rectangle?
400
900
225
625
225
Given: Perimeter of the rectangle = 80 cm, Ratio of sides (length:width) = 5:3.
Perimeter of the rectangle = 80 cm, Ratio of sides (length:width) = 5:3.
P=2├Ч(l+w),Area=s2
Sum of ratio parts is 5+3=8. Since perimeter is 2(l+w)=80, then l+w=40. The length is 85тАЛ├Ч40=25.
Students often calculate the area of the rectangle (15imes25=375) instead of the area of the square whose side is the rectangle's length.
Define sides using ratio
Let the length l=5x and width w=3x.
l=5x,w=3x
Solve for x using perimeter
The perimeter of a rectangle is 2(l+w)=80. Substituting the values: 2(5x+3x)=80.
16x=80тЯ╣x=5
Calculate length of the rectangle
The length is l=5x. Substituting x=5 gives l=5├Ч5=25 cm.
l=25
Calculate area of the square
The square side is equal to the rectangle's length, so side=25 cm. The area is side2=252.
252=625
D is correct because the length of the rectangle is 25 cm, and the area of a square with side 25 cm is 25├Ч25=625 sq cm.
Understanding ratios is essential for problems involving mixtures and work-time, where total values are divided in given proportions.