similarity question 12

Question

An Olympic standard swimming pool is a rectangle that measures 50 meters in length and 25 meters in width. A scale model of the pool is built using a scale of 2.5 in : 10 m.

a) Find the length and width of the scale model. DO NOT ROUND. Leave as a decimal.

length = ?  inches

width = ?  inches

b) Find the perimeter of the actual pool.

 ? meters

c) Find the perimeter of the scale model.

? inches

Answer 1

Let L = the length of the scale model

meters/inches: 10/2.5 = 50/L

Cross multiply.

10L = 125

L = 12.5 inches

Let w = the width of the scale model

10/2.5 = 25/w

10w = 62.5

w = 6.25 inches

Perimeter of actual pool:

P = 2l + 2w

P = 2(50) + 2(25)

P = 100 + 50

P = 150 meters

Perimeter of Scale Model:

P = 2(12.5) + 2(6.25)

P = 25 + 12.5

P = 37.5 inches