Question

A scale drawing of a living room is shown below. The scale is 1 : 40. A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 4 inches. Show your work to determine the area of the room in square feet. i will give 12 point for the right answer or i am reporting your answer if it is not correct.

Answer 1

The scale ratio of a point A to another point B is the division of the length of B by the length of A. The area of the room is approximately 266.67 square feet.

Given that:

$Scale = 1:40$

$l = 6in$ --- length of rectangle

$w = 4in$ --- width of rectangle

Divide by 12 to convert the dimensions to feet

$l = \frac{6}{12}ft$

$w=\frac{4}{12}ft$

$Scale = 1:40$ means that the dimension of the room is 40 times the dimension of the rectangle.

So, we have:

$Length = \frac{6}{12}ft * 40 = 20ft$

$Width = \frac{4}{12}ft * 40 = \frac{40}{3}ft$

The area of the room is:

$Area = Length * Width$

So, we have:

$Area = 20ft * \frac{40}{3}ft$

$Area = \frac{800}{3}ft^2$

$Area = 266.67ft^2$

The area of the room is 266.67 square feet

Read more about scale ratios at:

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