Question

2 similar cardboards have areas of 24cm square and 150cm square. if the length of the bigger one is 10cm, what is the length of the smaller one​

Answer 1

4 cm

Explanation:

Given 2 similar figures with sides in ratio a : b , then

ratio of areas = a² : b²

let n be the length of the smaller one , then

ratio of sides = n : 10

ratio of areas = n² : 10² = n² : 100

Using proportion

(
`(ratio)/(area)` )

`(n^2)/(24)` =
`(100)/(150)` =
`(2)/(3)` ( cross- multiply )

3n² = 48 ( divide both sides by 3 )

n² = 16 ( take the square root of both sides )

n =
`√(16)` = 4

length of the smaller one is 4 cm