A square has a side $5$ centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square.

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Solution

From the given information, we take the dimension of the smaller square as $x$ , and hence we get the dimension of the larger square as $y$ or $x + 5$
Again as per the information given, the area of the larger square is equal to four times the area of the smaller square, we get the equation,
$4 x^{2} = x^{2} + 10 x + 25$
or ${3 x}^{2} = 10 x + 25$
or ${3 x}^{2} - 10 x - 25 = 0$
By factorizing this trinomial we get the factors as
$(x - 5) (3 x + 5) = 0$
Now to make this equation true, we have to take the value of $x$ such that one of the factors result in 0 and this value has to be a positive number , because the dimensions cannot be in negative, we are left with just one choice of taking $x$ as 5 in the first factor as 5 to make it zero and hence the whole LHS to zero.
after putting the value of $x$ we get the equation as,
$(5 - 5) (3 x + 5) = 0$
Now LHS = RHS,
Hence the dimension of the smaller square $x$ is 5cm and the dimension of the larger square $y$ is $x + 5$ = 10cm
So the answer is
the dimension of the smaller square is 5cm and
the dimension of the larger square is 10cm.

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A square has a side 5 centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square.

A square has a side $5$ centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square.