geometric progfession

Question

the length of the sides of a triangle are in geometric progression. the length of the shortest side is 6 cm and the perimeter of the triangle is 28 1/2 cm. find the length of the sides?

Answer 1

The lengths of the sides are a, ar and ar² so the perimeter is a(1+r+r²)=28.5cm, where a=6cm and r is the common ratio for the geometric sequence.

1+r+r²=28.5/6=4.75,

r²+r=3.75,

r²+r+0.25=4,

(r+0.5)²=2²,

r+0.5=2, r=1.5. The side lengths are 6cm, 9cm, 13.5cm.