Question

The rectangular floor of a classroom is 30 feet in length and 40 feet in width. A scale drawing of the floor has a length of 15 inches. What is the area, in square inches, of the floor in the scale drawing?

Answer 1

The area of the scale drawing is 300in²

Explanation:

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Another way to think of this:

1 foot = 12 inches. Convert everything to inches.

`30ft*(12 inch)/(1 ft) \\= 30*12in \\= 360in\\\\`

`40ft*(12in)/(1ft) \\=40 * 12in \\= 480in\\`

These are the dimensions in inches of the REAL floor. The scaled drawing has dimensions of 15 inches for the length. To find the scale factor, divide the initial length by this.

`(360in)/(15in) = 24\\`, so the initial length was scaled down 24 times. Use this scalar for the width to find the scaled width.

`(480in)/(24) = 20in`, so the width of the drawing is 20 inches.

Area = L * W for a rectangle, so:

`15in *20in = 300in^(2)`