A scale diagram of a building has a height of 3 cm. The real-life building has a height of 42 m. Tim has tried to work out the scale of the diagram as a ratio in its simplest form. a) Write a sentence to explain the mistake Tim has made. b) Work out the correct ratio.

1. Problem Description

A scale diagram of a building has a height of 3 cm. The real-life building has a height of 42 m. Tim has tried to work out the scale of the diagram as a ratio in its simplest form.

a) Write a sentence to explain the mistake Tim has made.

b) Work out the correct ratio.

2. Solution Steps

a) Tim's mistake was that he didn't convert the units to be the same before simplifying the ratio. He divided both sides of the ratio by 3 without converting meters to centimeters first. The ratio should be in the same units.

b) To find the correct ratio, we need to convert the meters to centimeters.

We know that 1 meter is equal to 100 centimeters.

Therefore, 42 meters is equal to $42 \times 100 = 4200$ centimeters.

So, the ratio of the diagram to the real-life building is 3 cm to 4200 cm, which can be written as $3:4200$.

Now, we can simplify the ratio by dividing both sides by their greatest common divisor, which is

3. $3 \div 3 = 1$

$4200 \div 3 = 1400$

So, the simplified ratio is $1:1400$.

3. Final Answer

a) Tim did not convert the units to be the same before simplifying the ratio.

b) The correct ratio is $1:1400$.