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?
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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.
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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Consider sides as a, ar, ar^2 (in GP)
Sum of sides = a + ar + ar^2 = 37
=> a(1+r+r^2) = 37
a=9(shortest side)
=> r + r^2 = 28/9
=> 9r^2 + 9r - 28 = 0
=> 9r^2 + 21r - 12r -28 = 0
=> 3r(3r + 7) -4(3r + 7)= 0
=> r is either 4/3 or -7/3
Sides belong to +Z(integers)
Therefore sides are 9, 9*4/3, 9*4/3*4/3 => 9, 12, 16
good evening__________✌️✌️✌️✌️
Consider sides as a, ar, ar^2 (in GP)
Sum of sides = a + ar + ar^2 = 37
=> a(1+r+r^2) = 37
a=9(shortest side)
=> r + r^2 = 28/9
=> 9r^2 + 9r - 28 = 0
=> 9r^2 + 21r - 12r -28 = 0
=> 3r(3r + 7) -4(3r + 7)= 0
=> r is either 4/3 or -7/3
Sides belong to +Z(integers)
Therefore sides are 9, 9*4/3, 9*4/3*4/3 => 9, 12, 16
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