Question

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 5 meters longer than each side of the square. Find the dimensions of the garden.

Answer 1

We know:

the triangle gardern(garden A) and the square garden(garden B) have the same perimeter.

This may sound obv, but it's important: garden A has 1 less side then garden B, which is why it can have longer sides but the same perimeter.


So side A1 + side A2 + side A3 = side B1 + side B2 + side B3 + side B4.


A1 + A2 + A3 = B1 + B2 + B3 + 15(the extra length on the triangle sides)

Since B is a square, B = 15 m by 15 m.

I don't know enough about triangle to put the dementions, but it's an equilateral triangle so the sides are 20 m each. Hope that helps! :)

Answer 2

Answer: Dimension of square = 15 meters

Dimension of equilateral triangle = 20 meters

Explanation:

Let the side-length of square be "x".

Then , the perimeter of square will be :_

`\text{Perimeter of square=4(side) =4x}`

Then, the side-length of the equilateral triangle will be 5+x.

`\text{Perimeter of equilateral triangle=3(side) =3(5+x)}`

Since, the both gardens will require the same amount of fencing​ (both gardens have the same perimeter in​ meters).

i.e.
`3(5+x)=4x`

`\Rightarrow\ 15+3x=4x\\\\\Rightarrow\ 4x-3x=15\\\\\Rightarrow\ x=15`

Then, dimension of square = 15 meters

Dimension of equilateral triangle =
`5+15=20\text{ meters}`