Question

1. the ratio of the lengths of corresponding sides of two similar rectangles is 4:7. the smaller rectangle has an area of 64 square centimeters. what is the area of the larger rectangle?

Explanation:

Step1: Find area ratio

For similar figures, the ratio of areas is the square of the ratio of corresponding sides.
Ratio of sides = $4:7$, so area ratio = $4^2:7^2 = 16:49$

Step2: Set up proportion

Let $A$ = area of larger rectangle.
$\frac{64}{A} = \frac{16}{49}$

Step3: Solve for $A$

Cross-multiply: $16A = 64 \times 49$
$A = \frac{64 \times 49}{16}$
$A = 4 \times 49 = 196$

Answer:

196 square centimeters