How to calculate the area of both squares?

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Answer 1 · 2018-04-21T00:03:16

Read below.

Since the first piece of the #10#-meter string is cut into two pieces (the first one being#x# meter long), the other piece is #10-x# meters long.

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

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

We apply the same steps to the second square:

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

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

We add the areas together:

#=>x^2/16+(x^2-20x+100)/16#

#=>(2x^2-20x+100)/16# Simplify.

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

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

That matches what the problem presented us with.