Question

One side of a triangle is 7 cm and the perimeter of the triangle is 18 cm. If the

area of the triangle is √108cm²

, find the other two sides of the triangle.​

Answer 1

Answer:

Perimeter of the triangle = 18 cm

half perimeter= 18cm/2=9 cm

one side = 7 cm , so that sum of second and third Side = 18cm-7cm=11cm

let second side be x

so that third Side = 11-x

area of triangle using Heron's formulae

=√s(s-a)(s-b)(s-c)

√9(9-7)(9-x)(9-11+x)=√108

√9×2(9-x)(9-11+x)=√108

18×(9-x)(9-11+x)=108

9x-18-x^2+2x=6

-x^2+11x-18=6

-x^2+11x-24=0

x^2-11x+24=0

x^2-8x-3x+24=0

x(x-8)-3(x-8)=0

(x-3)(x-8)=0

now, x-3=0

x=3cm

so that second side=11cm-3cm=8cm

hope it helps you

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