Question

5. Each of the sides of a triangle is 8 cm less than the sum of its other two sides. Area of the triangle (in cm²) is?

pls give correct explaination to this

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Answer 1

Answer:

16∛ cm²

Step-by-step explanation:

Let a,b,c be the sides of a triangle.

a=b+c−8=____ (1)

b=a+c−8=____ (2) and  

c=a+b−8=____ (3)

Substituting (2),(3) in (1) we get

a=b−c+24 =___ (4)

Add (1) and (4) we get

a=8 cm

Similarly  b=8 cm, c=8 cm

Since the sides are equal, the triangle is equilateral triangle.

Area of equilateral triangle = $\frac{\sqrt3}{4}$×side²

                                             =$\frac{\sqrt3}{4}$×64

                                             =16∛ cm²

therefore, area of triangle is 16∛ cm².