Question

Which of the following options is correct?
Rectangle A: $Length=\frac{5}{9}in,Width=\frac{7}{4}in$

Rectangle B: $Length=\frac{20}{18}in,Width=\frac{5}{2}in$

• A. Area of rectangle A = Area of rectangle B
• B. Area of rectangle A < Area of rectangle B
• C. Area of rectangle A > Area of rectangle B
• D. Area of rectangle A = Area of rectangle B = $0$

Answer 1

The correct option is B Area of rectangle A < Area of rectangle B

Rectangle A:
$Length=\frac{5}{9}in,Width=\frac{7}{4}in$
Area of rectangle $A=\frac{5}{9}in\times \frac{7}{4}in=\frac{5\times 7}{9\times 4}=\frac{35}{36}sqin$

Rectangle B:
$Length=\frac{20}{18}in,Width=\frac{5}{4}in$
Area of rectangle $B=\frac{20}{18}in\times \frac{5}{4}in=\frac{20\times 5}{18\times 4}=\frac{100}{72}sqin$
To compare the fractions, we need to ensure they have the same denominators.

Rectangle A:
$\frac{35}{36}sqin=\frac{35\times 23}{6\times 2}=\frac{70}{72}sqin$
Rectangle B:
$\frac{100}{72}sqin$

$\frac{70}{72}sqin<\frac{100}{72}sqin$
Area of rectangle A < Area of rectangle B
Hence, option B is correct.