If figure B is similar to figure A by a scale factor, then the area of B is equal to the area of A times the square of the scale factor.
288 square inches and 648 square inches
Practice makes perfect
We are given that the sides of three similar rectangles are in the ratio 1:2:3.
This means that the size of the medium rectangle is 2 times the size of the smallest rectangle and the size of the largest rectangle is 3 times the size of the smallest rectangle. We want to find the area of the medium and the largest rectangles knowing that the area of smallest one is 72 square inches. Let's start by recalling the relationship between the areas of similar figures.
Area of Similar Figures
If figure B is similar to figure A by a scale factor, then the area of B is equal to the area of A times the square of the scale factor.
We can use this fact to calculate the desired areas. We will start with the area of the medium rectangle. According to the given rule, the area of the medium rectangle is equal to the area of the smallest rectangle times the scale factor raised to the second power. In this case, the scale factor is 2.
Area of the medium rectangle = 72 ( 2)^2 = 72(4) = 288
Therefore, the area of the medium rectangle is 288 square inches. Next, we will find the area of the largest rectangle. Similar as before, the area of the largest rectangle is equal to the area of the smallest rectangle times the scale factor raised to the second power. In this case, the scale factor is 3.
Area of the largest rectangle = 72 ( 3)^2 = 72(9) = 648
We got that the area of the largest rectangle is 648 square inches.
