Question

The lengths of the sides of a triangle form a G.P. If the perimeter of the triangle is 37 cm and the shortest side is of length 9 cm, find the lengths of the other two sides. 5.1 Sum of first n terms of a Gp​

Answer 1

Answer:

your answer is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : \\ lengths \: of \: remaining \: two \: sides \\ of \: triangle \\ \\ so \: since \: for \: a \: certain \: triangle \\ its \: three \: sides \: are \: in \: G.P \\ let \: the \: three \: sides \: be \\ a,ar,ar {}^{2} \\ \\ a = 9 \: \: \: \: \: \: (given) \\ \\ a + ar + ar {}^{2} = 37 \\ 9 + 9r + 9r {}^{2} = 37 \\ 9r {}^{2} + 9r - 28 = 0 \\ 9r {}^{2} + 21r - 12r - 28 = 0 \\ 3r(3r + 7) - 4(3r + 7) = 0 \\ (3r + 7)(3r - 4) = 0 \\ \\ r = - \frac{7}{3} \: \: or \: \: r = \frac{4}{3}$

$since \: side \: of \: any \: geometric \: figure \\ can \: never \: be \: negative \\ r = - \frac{7}{3} \: \: is \: absurd \\ \\ r = \frac{4}{3} \\ \\ hence \: here \\ ar = 9 \times \frac{4}{3} = 12 \\ \\ ar {}^{2} = 9 \times ( \frac{4}{3} \: ) {}^{2} = 16 \\ \\ thus \: remaining \: two \: sides \: are \: \\ 12.cm \: and \: 16.cm$