Question

The linear scale factor of two similar shapes is in ratio 3:4 if the area of the smaller shape is 72cm, find the area of the bigger shape

Answer 1

Answer:

128 cm²

Step-by-step explanation:

Given linear scale factor of 2 similar shapes = a : b , then

ratio of areas = a² : b²

Here linear scale factor = 3 : 4 , then

ratio of areas = 3² : 4² = 9 : 16

let x be the area of the larger shape then by proportion

$\frac{9}{72}$ = $\frac{16}{x}$ ( cross- multiply )

9x = 1152 ( divide both sides by 9 )

x = 128

That is area of larger shape is 128 cm²