Maths help needed, Ratio?

Question

A floor plan of a house has been drawn to a scale of 1: 200.

a. If a lounge room is actually 4m by 3.5m, what would its dimensions be on the plan? Give your answer in mm.

b. Would a car 1.8m wide and 5m long fit in the garage if on the plan the garage is 15mm by 30mm?

Answer 1

Part a)
4 m--->4000 x 1 / 200 mm = 20 mm
3.5 m-->3500 x 1 / 200 mm = 17.5 mm

Part b
1.8 m-->1800 x 1/200 mm = 9 mm
5 m--->5000 x 1/200 mm = 25 mm
Car would fit on plan.

Answer 2

a. 4m x 3.5m = 4000mm x 3500mm
scale 1:200 = 4000/200 x 3500/200
=20mm x 17.5mm

b. scale 1:200 = 15mm x 200 & 30 x 200
= 3000mm x 6000mm
=3m x 6m
yes

Answer 3

In words. let x = the unknown measurement on the floor plan.
then: x is to 4m as 1 is to 200
math representation: x/4m = 1/200
x = 4m/200 = .02m = 20mm
Therefore 20 mm on the floor plan = 4 m in the actual room.

You do the others.

Answer 4

1. 20 mm , 17.5 mm

To do this simply divide 4m and 3.5m by 200 (because of the ratio) , and then multiply by 1000 (m to mm conversion). Or you can simply multiply by 5 as the ratio of 1000/200 is 5.

2. Yes

To do this multiply 15mm and 30 mm by 1/5; multiply by 200, then divide by 1000. (1/5)

Answer 5

1:200 = x:(4 * 3.5)
1:200 = x:14

200x = 14
x = 7/100

=7/100 * 100 * 10
= 70

a. Answer: 70 mm

Width of garage plan in meters:
= 15 * (100 * 10) / 1000
= 1.5

Length of garage plan in meters:
= 30 * (100 * 10) / 1000
= 30

Answer: No it won't fit because the width is short to accomodate the actual width of the car.

Answer 6

A.
1/200

4m*3.5m = 4000mm *3500mm

(4000mm *3500mm)/200

20mm*17.5mm

B.
1.8m *5m = 1800mm * 5000mm

(1800mm * 5000mm)/200

9mm *25mm car

15mm * 30mm garage

Yes car fits!