if for the triangle whose perimeter is 37cm and length of sides are in G. p. also the length of the smallest side is 9cms.then length of remaining two sides are-
a) 12,16 b) 14,14 c) 10,18 d) 15,13
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Given that the sides of the triangle are in G.P.
Let the sides of the triangle be a,ar,ar
2
.
As we know that the perimeter of a triangle is equal to the sum of all sides of triangle.
Therefore,
a+ar+ar
2
=37.....(1)
Given that the length of the shortest side is 9cm.
Therefore,
a=9
Substituting the value of a in eq
n
(1), we have
9+9r+9r
2
=37
⇒9r
2
+9r−28=0
⇒9r
2
+21r−12r−28=0
⇒3r(3r+7)−4(3r+7)=0
⇒(3r+7)(3r−4)=0
⇒r=−
3
7
or r=
3
4
Since sides of triangle cannot be negative.
⇒r
=−ve
∴r=
3
4
Thus, sides of triangle are 9cm,12cm and 16cm
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