1.

the length of the sides of a triangle form a G.P. If the perimeter of the triangle is 37cm and the shortest side is of length 9 cm, find the length of the other two sides?

Answer»

The 3 sides of the triangle are a, ar and ar^2 and while a = 9 the sum is 37 cm.

S3 = a(R^n-1)/(r-1), or

37 = 9(r^3–1)/(r-1) = 9(1+r+r^2) = 9 +9R+ 9 r^2, or

28=9r+9r^2, or

9r^2+9r-28=0

9r^2+21r-12r-28 = 0

3r(3r+7) - 4(3r+7) = 0

(3r-4)(3r+7) = 0

Or r = 4/3 or -7/3.

So the THREE sides are 9, 9*4/3 or 12, and 12*4/3 or 16.

The three sides are 9 cm, 12 cm and 16 cm.


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