Square Area Calculation: Finding Area B Using 2/3 Ratio and 56-Unit Perimeter

Question

Square A is greater than square B by a ratio of $\frac{2}{3}$ .

If the perimeter of square A is known to be 56, what is the area of square B?

00:00 Find the area of square B

00:03 In a square all sides are equal, marked as A

00:11 The square perimeter equals the sum of its sides

00:15 This is the side length in square 1

00:24 Side ratio according to the given

00:32 We'll substitute square 1 side value to find Y

00:40 We'll multiply by the inverse to isolate Y

00:45 This is side length Y

00:52 Square area equals side squared

01:01 And this is the solution to the question

We will mark the side in square A as X

Therefore the perimeter will be:
$4x=56$

$x=14$

Now we can calculate the area of square A:

$14\times14=196$

As we are given the ratio between the areas:

$\frac{196}{S_2}=(\frac{2}{3})^2=\frac{4}{9}$

That is, the ratio will be:

$\frac{196}{X}=\frac{4}{9}$

The area of the square will be equal to:

$\frac{9\times196}{4}=\frac{1764}{4}=441$

441