Question

The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. draw another scale drawing of the pool using the scale 25 m to 2 cm. Explain why your drawing is accurate.

Answer 1

Explanation:

From the given rectangle,

Length of the rectangle = 5 cm

Width of the rectangle = 10 cm

Ratio of length : width = 1 : 2

Perimeter of the rectangle = 2(l + b)= 150 cm

l + b = 75 -----(1)

Since, l : b = 1 : 2

`(l)/(b)= (1)/(2)`

b = 2l ------(2)

From equations (1) and (2),

l + 2l = 75

3l = 75

l = 25 m

Width 'b' = 2(25) = 50 m

Now we have to draw a rectangle with a scale = 25 : 2

Therefore, Scale factor =
`(25)/(l)=(25)/(2)`

l = 2 cm

Similarly,

`(50)/(w)=(25)/(2)`

w = 4 cm

Now we can draw a rectangle with length = 2 cm and width = 4 cm.