The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. find the side of the square, if it’s known that the area of the square is 30 cm2 less than the area of the rectangle. quickly 10 points

By writing and solving a system of equations, we want to find the side of the given square. We will see that the side length of the square is S = 5.52cm

Let's see how to solve the problem:

So we know that the side of the square, S, is 3cm smaller than one side of a rectangle, L, and 2 cm greater than the other side of the rectangle, W.

So we can write this as:

We also know that the area of the rectangle is 30cm^2, remember that the area is just the product between the measures of both sides, so we have:

L*W = 30cm^2

We can write this as:

L = (30cm^2)/W

And replace it on the first equation to get the system of equations:

So now we have two equations and two variables.

We want to find the value of S, so we can isolate W in one of the equations, if we isolate W in the second one we get:

W = S - 2cm

Now we can replace this on the first equation to get:

S = (30cm^2)/(S - 2cm) - 3cm

Now let's multiply both sides by (S - 2cm)

S*(S - 2cm) = 30cm^2 - 3cm*(S - 2cm)

S^2 - 2cm*S = 30cm^2 - 3cm*S + 6cm^2

Moving all the terms to the same side we get:

S^2 + 1cm*S - 36cm^2 = 0

This is just a quadratic equation, the solutions are given by:

We only care for the positive solution, which is:

S = (-1cm + 12.04cm)/2 = 5.52cm

Concluding, the side length of the square is 5.52cm

If you want to learn more about systems of equations you can read:

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