Question

A picture has an area of 35cm and is 7cm long.An enlargement of the picture is made which is 21cm long.Find the area of the enlargement​

Answer 1

increase by a factor of 3

Explanation:

First you have to find the width,

35/7=5cm

Since the length had been increased to 21cm, we need to find the larger area,

21*5=105cm^2

now we just need to find how much has the area increased compare to the original area,

105/35=3

Answer 2

315 cm²

Explanation:

Given the scale factor of 2 similar figures is a : b , then

ratio of areas = a² : b²

Here the scale factor = 7 : 21 = 1 : 3 , thus

ratio of areas = 1² : 3² = 1 : 9

That is the area of the enlargement is 9 times the original, so

area of enlargement = 35 × 9 = 315 cm²