Determine which of the following rectangles has the least area among the four.
Rectangle A:Length=74 cm, Width=75 cm
Rectangle B:Length=45 cm, Width=74 cm
Rectangle C:Length=23 cm, Width=32 cm
Rectangle D:Length=54 cm, Width=23 cm
A
Rectangle B
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B
Rectangle A
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C
Rectangle D
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D
Rectangle C
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Solution
The correct option is C Rectangle D Rectangle A Length=74 cm, Width=75 cm Area=Length×Width =74×75=7×74×5=4920 sq cm
Rectangle B Length=45 cm, Width=74 cm Area=Length×Width =45×74=4×75×4=2820 sq cm
Rectangle C Length=23 cm, Width=32 cm Area=Length×Width =23×32=2×33×2=66=1 sq cm
Rectangle D Length=54 cm, Width=23 cm Area=Length×Width =54×23=5×24×3=1012 sq cm
To compare the fractions, we have to make them have the same denominators.
Rectangle A 4920sqcm=49×320×3=14760 sq cm
Rectangle B 2820 sq cm = 28×320×3=8460 sq cm
Rectangle C 1 sq cm =1×601×60=6060 sq cm
Rectangle D 1012 sq cm =10×512×5=5060 sq cm
14760>8460>6060>5060
Rectangle A > Rectangle B > Rectangle C > Rectangle D
So, Rectangle D has the leastest area.
Hence, option D is correct.