Answer:
m = 8
n = 9
Explanation:
Remark
By similar triangles
(m - 4) /8 = 8 / 2m Cross multiply
2m(m - 4) = 64 Expand the left
2m^2 - 8m = 64 Divide through by 2
m^2 - 4m = 32 Subtract 32 from both sides.
m^2 - 4m - 32 = 0 Factor
(m - 8)(m + 4) = 0
m + 4 has no meaning in geometry. - numbers cannot be distances.
m - 8 = 0
m = 8
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By the same kind of similar triangles used in problem A we get
7 / x = x / 9
x^2 = 63
Just leave this as it is. We'll solve this by the Pythagorean Theorem.
x^2 + 9^2 = (n + 3)^2
63 + 81 = (n + 3)^2
144 = (n + 3)^2 Take the square root of both sides
12 = n + 3 Subtract 3 from both sides.
9 = n