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

Square A is greater than square B by a ratio of 23 \frac{2}{3} .

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

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Step-by-step video solution

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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

Step-by-step written solution

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1

Understand the problem

Square A is greater than square B by a ratio of 23 \frac{2}{3} .

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

2

Step-by-step solution

We will mark the side in square A as X

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

x=14 x=14

Now we can calculate the area of square A:

14×14=196 14\times14=196

As we are given the ratio between the areas:

196S2=(23)2=49 \frac{196}{S_2}=(\frac{2}{3})^2=\frac{4}{9}

That is, the ratio will be:

196X=49 \frac{196}{X}=\frac{4}{9}

The area of the square will be equal to:

9×1964=17644=441 \frac{9\times196}{4}=\frac{1764}{4}=441

3

Final Answer

441

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