# The sum of the areas of the rectangle and the square is 2x^2+ 4x +1. Given that this sum is 49 cm^2, how do you find x and the area of the square?

Nov 28, 2016

$2 {x}^{2} + 4 x + 1 = 49$

$2 {x}^{2} + 4 x - 48 = 0$

$2 \left({x}^{2} + 2 x - 24\right) = 0$

${x}^{2} + 2 x - 24 = 0$

$\left(x + 6\right) \left(x - 4\right) = 0$

$x = - 6 \mathmr{and} 4$

We disregard the negative solution. So, $x = 4$.

I don't think there is enough information to definitively find the area of the square.

Hopefully this helps!