Question

An interior designer sketches a design for a rectangular rug. The dimensions of the sketch are 4in. by 7.5 in. The dimensions of the actual rug will be ten times the dimensions of the drawing, so the scale of the drawing is 1:10. How many times the area of the sketch is the area of the actual rug?

- Which figures in the problem are similar? What are their dimensions?
- How can proportions help you find the dimensions of the actual rug?

Answer 1

Similar figures are a rectangular sketch and a rectangular rug. Dimensions of the sketch are:
W ( width ) = 4 in, L ( length ) = 7.5 in.
Proportions are:
W (sketch) : W(rug) = 1 : 10
L ( sketch) : L (rug) = 1 : 10
W (rug) = 10 * 4 = 40 in
L (rug) = 10 * 7.5 = 75 in
A (sketch) = 4 * 7.5 = 30 in²
A (rug) = 40 * 75 = 3,000 in²
3,000 : 30 = 100
Answer: Area of the actual rug is 100 times the area of the sketch.