Question

The lengths of the sides of a triangle are (2a+1) cm, (3a+2) cm and (4a-1) cm, for what value of 'a' is the perimeter of the triangle 92 cm

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Answer 1

Answer:

(2a + 1 ) + ( 3a + 2 ) + (4a - 1 ) = 92

9a + 2 = 92

9a = 92 - 2

9a = 90

a = 90/9

a = 10

Answer 2

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$\implies$ 2a + 1 + 3a + 2 + 4a - 1 = 92

$\implies$ 2a + 3a + 4a + 1 + 2 - 1 = 92

$\implies$ 9a + 3 - 1 = 92

$\implies$ 9a + 2 = 92

$\implies$ 9a = 92 - 2

$\implies$ a $= \frac{90}{9}$

$\implies$ a = 10

$\therefore$ length of 1st side = $2a\:+\:1 \\ 2\:×\:10\:+1 \\ 21$

$\therefore$ length of 2nd side = $3a\:+\:2 \\ 3\:×\:10\:+\:2 \\ 32$

$\therefore$ length of 3rd side = $4a\:-\:1 \\ 4\:×\:10\:-\:1 \\ 39$