Explanation:
the length of the diagonal is calculated out of the length and width by using Pythagoras (after all, one length, one width and the diagonal are creating a right-angled triangle).
25² = length² + width²
length = 2×width + 10
we are using the second in the first equation :
25² = (2×width + 10)² + width²
625 = 4×width² + 40×width + 100 + width²
525 = 5×width² + 40×width
105 = width² + 8×width
width² + 8×width - 105 = 0
a quadratic equation
ax² + bx + c = 0
has the general solutions
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = 1
b = 8
c = -105
width = (-8 ± sqrt(8² - 4×1×-105))/(2×1) =
= (-8 ± sqrt(64 + 420))/2 =
= (-8 ± sqrt(484))/2 =
= (-8 ± 22)/2 = -4 ± 11
width1 = -4 + 11 = 7
width2 = -4 - 11 = -15
a negative size of the length of a side of a shadow does not make any sense, so, our valid solution is
width = 7 in.
and then
length = 2×width + 10 = 2×7 + 10 = 14 + 10 = 24 in.