SOLUTION: The side length of square A is 36 cm. The side length of square B is 42 cm. What is the ratio of the area of square A to the area of square B? Express your answer as a common fract

Algebra ->  Equations -> SOLUTION: The side length of square A is 36 cm. The side length of square B is 42 cm. What is the ratio of the area of square A to the area of square B? Express your answer as a common fract      Log On


   

Question 1151194: The side length of square A is 36 cm. The side length of square B is 42 cm. What is the ratio of the area of square A to the area of square B? Express your answer as a common fraction.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The side length of square A is 36cm.
the area of square A is %2836cm%29%5E2=1296cm%5E2
The side length of square B is 42cm.
the area of square B is %2842cm%29%5E2=1764cm%5E2
the ratio of the area of square A to the area of square B is:
A%2FB=1296cm%5E2%2F1764cm%5E2
A%2FB=1296%2F1764
A%2FB=36%2F49=> answer



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by tutor @MathLover1 is perfectly good... but it involves calculations much more complicated than necessary. The solution can be achieved much more easily using a basic fact about similar figures.

All squares are similar. The ratio of the side lengths of the two squares is 36:42 = 6:7.

In any similar figures, the ratio of area measurements is the square of the ratio of the linear measurements. So the ratio of the areas of these two squares is 6^2:7^2 = 36:49; or, expressed as a common fraction, 36/49.