Question

A triangle has integer sides. One side is three times a second side. The length of the third side is 15.

The greatest possible perimeter of the triangle is

• A. 43
• B. 46
• C. 48
• D. 52

Answer 1

The correct option is A

43

1.Let a, 3a, 15 be the lengths of the sides

a + 3a > 15 $\Rightarrow$ a > 3.75 i.e., a ≥ 4 ( a - an integer )--------- (1)

3a < a + 15 $\Rightarrow$ 2a < 15,a < 15/2= 7.5

∴a ≤ 7--------------------------------------------- ( 2 )

a = 4,5,6,7

Maximum perimeter occurs when a = 7

i.e., sides are 7, 21, 15.

Perimeter = 7 + 21 + 15 = 43.