Question

Each side of a triangle is 8cm less than the sum of its other two sides .what is the area of triangle?

Answer 1

Answer:

Step-by-step explanation:

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Given thatb+c−8=a ;

equation(i)c+a−8=b ;

equation(ii)a+b−8=c ;

equation(iii)Adding above three equations we get,

2(a+b+c)−24=a+b+c

⇒2(a+b+c)−(a+b+c)=24

⇒a+b+c=24

⇒b+c=24−a

Put this value in equation(i) we get,24−a−8=a⇒a+a=16⇒2a=16

⇒a=8 cm

Similarly b=c=8 cm⇒a=b=c=8 cm

Here it is an equilateral

triangle.⇒Area=3√4a2=3√482

⇒Area=3√4×64

⇒Area=163−−√ cm2

Let a,b,c be sides of the triangle.Given thatb+c-8=a ;

equationic+a-8=b ;

equationiia+b-8=c ;

equationiiiAdding above three equations we get,2a+b+c24=a+b+c

⇒2a+b+c-a+b+c=24

⇒a+b+c=24

⇒b+c=24-a

Put this value in equation in we get,24-a-8=a

⇒a+a=16

⇒2a=16

⇒a=8 cm

Similarly b=c=8 cm

⇒a=b=c=8 cm

Here it is an equilateral triangle.

⇒Area=34a2=3482

⇒Area=34×64

⇒Area=163 cm2

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