An interior designer sketches a design for a rectangular rug. the dimensions of a sketch are 4 inches 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 actual area of the rug? which figures in the problem are similar? what are the dimensions? how can proportions you find the dimensions of the actual rug?

3,000 in.

(4 x 10) + (7.5 x 10) = 3000

The dimensions on the sketch are 10 times less than the actual rug.

40 in., 7.5 in.

The drawing lengths are ten times more, so you just multiply the dimensions by 10, and then multiply the product you find out to find the actual area of the rug.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47