Question

Fred’s company is planning a new logo. The diagrams show two similar versions of the planned logo.

A) calculate the lengths of the sides marked a and b.
B) the smaller of the two versions of the logo costs £4.48 to paint with gold paint. Calculate the cost of the logo with the same gold paint.

Answer 1

A) a = 10.8, b = 4.2

B) £10.08

Explanation:

A) 7.5/5 = 1.5

a = 7.2 x 1.5 = 10.8

5/7.5 = 2/3

b = 6.3 x 2/3 = 4.2

B) 1.5 x 1.5 = 2.25

£4.48 x 2.25 = £10.08

Answer 2

a=7.2*1.5=10.8 cm

b=6.3/1.5=4.2 cm

`\pounds 4.48*2.25=\pounds 10.08`

Explanation:

Proportional Geometric Shapes

A) We are given two similar shapes of a logo. They are to be proportional. We only need to find the proportion ratio of two of them to find the rest of the lengths.

The upper sides have 7.5 cm and 5 cm respectively. This gives us the ratio

`\displaystyle r=(7.5)/(5)=1.5`

Which means all the measures of the smaller logo are 1.5 smaller than those of the larger. This means

b=6.3/1.5=4.2 cm

a=7.2*1.5=10.8 cm

B) To paint the logos, we need to cover its surface, so the ratio of the surface is 1.5*1.5=2.25

This means the cost to paint the larger logo is

`\pounds 4.48*2.25=\pounds 10.08`