Answer:
24
Explanation:
the lengths are in proportion to one another, between triangles.
(x - 4)/12 = 5/(x +7)
(x - 4)(x + 7) = 5 X 12
x² + 7x - 4x - 28 = 60
x² + 3x - 28 = 60
x² + 3x - 88 = 0.
(x + 11) (x - 8) = 0
x = -11, 8.
x cannot be -11 since both x +7 and x - 4 would be negative lengths!!
so x = 8.
AB = 12, DE = x - 4 = 8 -4 = 4. 12/4 = 3.
the lengths of triangle ABC are 3 times longer than the lengths of DEF.
we can confirm this: AC = x + 7 = 8 + 7 = 15. DF = 5
AC is 15/5 = 3 times longer than DF.
so we expect BC to be 3 times longer than x. x = 8.
so BC = 3 X 8 = 24.