The corresponding sides of two similar rectangles are 6 ft and 10 ft. The area of the smaller rectangle is 78 ft^2. To the nearest whole number, what is the area of the larger rectangle?
+130466 If the smaller rectangle has an area of 78 and a side of 6.......the other side = 78/6 = 13
So we have
6/13 = 10/x where x is the unknown side of the larger rectangle
Cross mutiply and we have
6x = 130 divide both sides by 6
x = 130/6 = 65/3
So....the area of the larger rectangle = 10*(65/3) = 650/3 = about 216.66 sq ft
Another way to see this is that the area of the larger rectangle is equal to the area of the smaller rectangle times the square of the ratio of the larger corresponding side to the smaller corresponding side
Thus:
78 * (10/6)^2 = 216.66 sq ft
