Universal Analysis of Equations (1702) - Page 25

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PROBLEM XI.

In a plane right-angled triangle, the sum of the hypotenuse and the perpendicular is given as 278 = s. The area is also given as 7269 = p. What is the base (a)?

An equation will arise: ssa — aaa = 4 s p
or ba — aaa = c

In numbers 77284a — aaa = 8083128.

Theor. x = (c + ggg - bg) / (b - 3gg)

g = 200

c + ggg — bg = + 626328

+ b — 3gg = — 42716 ) + 626328 ( — 14 = x

200

— 14

g = 186

c + ggg — bg = + 143160

+ b — 3gg = — 26504 ) + 143160 ( — 5.4 = x

186.

— 5.4

g = 180.6

c + ggg — bg = + 16152.216

+ b — 3gg = — 20565.08 ( + 16152.216 ( — .7854 = x

180.6

— .7854

g = 179.8146 or 179.814 = g

c + ggg — bg = + 322.299405144

+ b — 3gg = — 19715.224 ) + 322.299405144 ( — .016348 = x

179.814

— .016348

a = 179.797652