How to calculate the area of both squares?

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1 Answer
Apr 21, 2018

Read below.

Explanation:

Since the first piece of the 1010-meter string is cut into two pieces (the first one beingxx meter long), the other piece is 10-x10x meters long.

Since squares have the same side lengths, we say that the side length of the first square is x/4x4.

Using the formula A=l^2A=l2, we see that the area of the first square is (x/4)^2(x4)2 or x^2/16x216

We apply the same steps to the second square:

A=((-x+10)/4)^2A=(x+104)2

=>A=(x^2-20x+100)/16A=x220x+10016

We add the areas together:

=>x^2/16+(x^2-20x+100)/16x216+x220x+10016

=>(2x^2-20x+100)/162x220x+10016 Simplify.

=>(x^2-10x+50)/8x210x+508 We can rewrite this as:

=>1/8(x^2-10x+50)18(x210x+50)

That matches what the problem presented us with.