1.

If one side of a triangle is 7 with its perimeter equal to 18, and area equal to \(\sqrt {108} \), then the other two sides are:1. 3 and 82. 3.5 and 7.53. 7 and 44. 6 and 5

Answer» Correct Answer - Option 1 : 3 and 8

Given:

One side of triangle = 7 cm

Perimeter of triangle = 18 cm

Area of triangle = √108 cm2

Formula Used:

If sides of triangle are a, b, and c

then,

Semi perimeter (S) = (a + b + c)/2

Area of triangle = √[s(s - a)(s - b)(s - c)

Calculation:

18 = (7 + b + c)

⇒ (b + c) = 11

⇒ c = 11 - b 

S = 18/2 = 9

√108 = √[(9)(9 - 7)(9 - b)(9 - c)]

Squaring both sides,

108 = 18 × (9 - b) × (9 - c)

Substituting Value of c as 11 - b

6 = (9 - b)[9 - (11 - b)]

⇒ 6 = (9 - b)(b - 2)

⇒ 6 = 9b + 2b - b2 - 18

⇒ b2 - 11b + 24 = 0

⇒  b2 - 8b - 3b + 24 = 0

⇒ b(b - 8) - 3(b - 8) = 0

⇒ (b - 8)(b - 3) = 0

⇒ b = 8, 3

If we Take side b as 8

Then,

c = 11 - 8 = 3

∴ The other two sides of triangle are 8 cm and 3 cm.


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