Question

The perimeters of the square and the triangle shown below are equal. What is the value of x?

Answer 1

Perimeter is the sum of all the sides. So we can set up an equation:


`\sf 3x+1+3x+1+3x+1+3x+1=2x+8+x+8+4x+2`

Now solve for 'x', combine like terms:

When it comes to terms with variables it's just like normal addition but we keep the variable:


`\sf 3x+3x+3x+3x=12x`

`\sf 2x+x+4x=7x`

So we have:


`\sf 12x+1+1+1+1=7x+8+8+2`

Add:


`\sf 12x+4=7x+18`

Subtract 7x to both sides:


`\sf 5x+4=18`

Subtract 4 to both sides:


`\sf 5x=14`

Divide 5 to both sides:


`\boxed{\sf x=2.8}`