Question

The scale factor of two similar rectangles is 2:5. The area of the smaller rectangle is 8 m². What’s the area of the larger rectangle

Answer 1

area of larger rectangle = 50 m²

Explanation:

given the scale factor of 2 similar rectangles is a : b , then

scale factor of areas = a² : b²

here the scale factor = 2 : 5 , then

scale factor of their areas = 2² : 5² = 4 : 25

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

`(scale factor)/(area)`

`(4)/(8)` =
`(25)/(x)` ( cross- multiply )

4x = 8 × 25 = 200 ( divide both sides by 4 )

x = 50

the area of the larger rectangle is 50 m²