Question

Maggie created this scale drawing of a soccer field, using a scale factor of 1 inch : 12 yards. She wants to make another scale model of the same field, using a scale factor of 1 inch : 3 yards. Find the length and width of the new scale drawing.

Answer 1

The length and width of the new scale drawing is 36 inches and 24 inches respectively.

The given parameters:

• Original scale of the soccer field, 1 inch : 12 yards

The original length and width of the soccer field is calculated as follows;

1 inch : 12 yards

• original width = 6 x 12 yards = 72 yards
• original length = 9 x 12 = 108 yards

For the new scale of 1 inch : 3 yards, the new length and width are represented as;

the new width:

$\frac{1 \ inch}{x} = \frac{3 \ yards}{72 \ yards} \\\\x = 24 \ inches$

the new length:

$\frac{1 \ inch}{x} = \frac{3 \ yards}{108 \ yards} \\\\x = 36\ inches$

Thus, the length and width of the new scale drawing is 36 inches and 24 inches respectively.

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