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Two gardens are being fenced in. Both gardens will require the same amount of fencing​ (both gardens have the same perimeter in​ meters). One garden is in the shape of a square and the other is in the shape of an equilateral triangle. Each side of the triangle is 1 meters longer than each side of the square.

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thepingu

Answer:

The side length of the square is 3 meters.

The side length of the triangle is 4 meters.

Step-by-step explanation:

This is basically a systems of equations word problem.

To solve this, we have to create two different equations. Let's assume [tex]s[/tex] is the side length of the square and [tex]t[/tex] is the side length of the triangle.

We can make the equation [tex]4s=3t[/tex], since the perimeters are the same. (A square has 4 sides, a triangle has 3 - multiplying by the side length of each will get perimeter)

We also know that the side length of the triangle is 1 meter longer than the side length of the square, so the equation here becomes [tex]t = s+1[/tex].

Now, let's substitute the second equation ([tex]t = s+1[/tex]) into the first ([tex]4s=3t[/tex]).

[tex]4s = 3(s+1)[/tex]

Apply the distributive property:

[tex]4s = 3s+3[/tex]

Subtract 3s from both sides:

[tex]s=3[/tex]

So the side length of the square is 3. We can now plug it into the equation [tex]t = s + 1[/tex] to find the side length of the triangle.

[tex]t = 3+1\\\\t=4[/tex]

Hope this helped!

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