Question

3. Hessa is building a scale model of a park. She uses a scale of 12 cm to represent 1.5 m. a) The actual length of the bridge is 20 m. What is the length of the model bridge? b) In the model, the height of the climbing frame is 10 cm. What is the actual height of the frame?

Answer 1

The length of the model bridge is 160 cm and the actual height of the climbing frame is 1.25 m.

Step-by-step explanation:

To find the length of the model bridge, we can set up a proportion using the given scale. Let x represent the length of the model bridge. The proportion can be written as: 12 cm / 1.5 m = x cm / 20 m. Cross multiply and solve for x:

12 cm * 20 m = 1.5 m * x cm

240 cm*m = 1.5 m * x cm

Divide both sides by 1.5 m to isolate x:

x cm = 240 cm*m / 1.5 m

x cm = 160 cm

Therefore, the length of the model bridge is 160 cm.

To find the actual height of the climbing frame, we can set up another proportion. Let y represent the actual height of the frame. The proportion can be written as: 12 cm / 1.5 m = 10 cm / y m. Cross multiply and solve for y:

12 cm * y m = 1.5 m * 10 cm

12y = 1.5 * 10

12y = 15

Divide both sides by 12 to isolate y:

y = 15 / 12

y = 1.25 m

Therefore, the actual height of the climbing frame is 1.25 m.