A rectangular solar panel measures 108 cm by 45 cm. By adding the same amount to each dimension, the area is doubled. How much is added?

Let the amount added to each dimension be x. Then the new dimensions of the solar panel are (108+x) cm by (45+x) cm. The original area of the solar panel is (108)(45) = 4860 cm^2. The new area of the solar panel is twice the original area, so: 2(4860) = (108+x)(45+x) Expanding the right side: 9720 = 4860 + 153x + x^2 Simplifying: 0 = x^2 + 153x - 4860 Using the \quadratic formula: x = (-153 ± sqrt(23409))/2 x ? -153 or x ? 31.63 The negative solution doesn't make sense since we can't add a negative amount to each dimension. So the amount added to each dimension is \approx imately 31.63 cm. Verifying: The new dimensions of the solar panel are 139.63 cm by 76.63 cm. The new area of the solar panel is (139.63)(76.63) ? 9720 cm^2, which is twice the original area of 4860 cm^2.