# The side of a square is 4 centimeters shorter than the side of a second square. If the sum of their areas is 40 square centimeters, how do you find the length of one side of the larger square?

Let 'a' be the side of the shorter square. Then by condition, 'a+4' is the side of larger square. We know the area of a square is equal to the square of it's side. So ${a}^{2} + {\left(a + 4\right)}^{2} = 40$ (given) or $2 {a}^{2} + 8 \cdot a - 24 = 0$ or ${a}^{2} + 4 \cdot a - 12 = 0$ or $\left(a + 6\right) \cdot \left(a - 2\right) = 0$ So either $a = 2 \mathmr{and} a = - 6$ Side length canot be negative . $\therefore a = 2$. Hence the length of the side of larger square is $a + 4 = 6$ [Answer]