MATHS

[a+(15^2-a^2)^0.5]/[a+(20^2-a^2)^0.5]=3/4

4a + 4(225 - a^2)^0.5 = 3a + 3(400-a^2)^0.5
a + 4(225-a^2)^0.5 = 3(400-a^2)^0.5
a^2 + 8a(225-a^2)^0.5 + 16(225-a^2) = 9(400-a^2)
a^2 + 8a(225-a^2)^0.5 + 3600 - 16a^2 = 3600 - 9a^2
8a(225-a^2)^0.5 = 6a^2
4(225-a^2)^0.5 = 3a
16(225-a^2) = 9a^2
3600-16a^2 = 9a2
25a^2 = 3600
a^2 = 144
a = 12 or -12 (reject)

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