Question

What is the value of x if the perimeter of both shapes is the same?

Answer 1

The value of x is: $\frac{4}{3}$

Recall:

Perimeter of a shape is the sum of all its sides

Thus:

Perimeter of the triangle = $x + x +x+ 4 = 3x + 4$

Perimeter of the rectangle = $2(2x) + 2(x) = 4x + 2x = 6x$

We are told that the perimeter of both shapes are equal. Set both perimeters equal and solve for x.

$3x + 4 = 6x$

Add like terms

$4 = 6x - 3x\\4 = 3x$

Divide both sides by 3

$\frac{4}{3} = x\\x = \frac{4}{3}$

The value of $x = \frac{4}{3}$

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