Question

The difference between the semi perimeter and the sides of a triangle ABC are 8 cm , 7 cm , 5 cm respectively. Find the area of the triangle.

Answer 1

Let the semiperimeter = x

Side A's difference = 8 cm

Side B's difference = 7 cm

Side C's difference = 5 cm

Side A = x+8 cm

Side B = x+7 cm

Side C = x+5 cm

Now ,

x = (x+8+x+7+x+5)/2

x = 3x+20/2

2x = 3x+20

-x = 20

x= -20

But the semiperimeter can't be in negative.

Now Area of ∆ABC :

$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{20 \times 8 \times 7 \times 5}$

= 74.8331477 cm² = 74.833 cm² Approximately

Answer 2

HLO FRIEND______:-)

THE DIFFERENCE BETWEEN THE SEMI PERIMETER ___.....

=>> 
The difference between the semi-perimeter and the sides of triangle ABC are 8 cm, 7 cm and 5 cm, respectively. Find its semi-perimeter.

NOW___=>>>>SOLUTION<<<<<<<<

Let the semi-perimeter of the triangle be s. Let the sides of the triangle be a, b and c. Given: s – a = 8, s – b = 7 and s – c = 5Adding all the above equations, we get (s – a) + (s – b) + (s – c) = 8 + 7 + 5 ⇒ 3s – (a + b + c) = 20 ⇒ 3s – 2s = 20 [Since s = (a+b+c)/2] ⇒ s = 20 cm Thus the semi-perimeter is 20 cm
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