# A square with an area of 18cm^2 is placed beside a square with area 28cm^2 write a simplified expression for the perimeter of the shape.?

Hi! I'm having a lot of problems with these kinds of equations and i'd appreciate any help. Relevance

Let's ignore the areas for now and come up with an expression for the perimeter in terms of two variables:

x = side of the smaller square

y = side of the larger square

Looking at the shape, we see that three of the four small square's sides are exposed and three of the large square's sides are fully exposed.

So far we have:

3x + 3y

Then we have the little segment that is the difference between the larger and the smaller sides (y - x)  There is one of those. Add it to the previous expression:

3x + 3y + (y - x)

Now let's look at the areas.  The smaller is 18 cm² and the larger is 28 cm², so:

A = s²

18 = x² and 28  = y²

x = √18 and y = √28

x = √(9 * 2) and y = √(4 * 7)

x = 3√2 and y = 2√7

Now that we have values for x and y, substitute into our perimeter expression and simplify:

3x + 3y + (y - x)

3(3√2) + 3(2√7) + (2√7 - 3√2)

9√2 + 6√7 + 2√7 - 3√2

Combine line terms:

(6√2 + 8√7) cm

That is the length of the perimeter to the given shape.

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• Larger square has side length 2rt7 cm and smaller square has side length 3rt2 cm.

Examining picture, perimeter of resulting figure = [3{2rt7 +3rt2} + (2rt7-3rt2)] cm =

[8rt7 +6rt2] cm.

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• 1st solve the length of the square

A = s^2

18 = s^2

s = √(18)

s = √(9 * 2)

s = 3√(2)

solving the length of the 2ns square

28 = s^2

s = √(28)

s = √(4 * 7)

s = 2√(7)

Solving its perimeter

P = [2√(7) + 3√(2)] + 3√(2) + 3√(2) + [2√(7) - 3√(2)] + 2√(7) + 2√(7)

P = 6√(2) + 8√(7)  Answer//

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• Anonymous
1 month ago

here you are served • Log in to reply to the answers