Question

What do the following abbreviatior
stand for? P.O.
o post operations
o post office
o personal office
o private office​

Answer 1

Explanation:

Answer:

The semi perimeter ( s ) of the triangle is 30 cm.

Step-by-step-explanation:

We have given the subtraction of the sides of a triangle and the semi perimeter.

We have to find the semi perimeter of the triangle.

We have given that,

( s - a ) = 7 cm

( s - b ) = 8 cm

( s - c ) = 15 cm

Now,

( s - a ) + ( s - b ) + ( s - c ) = 7 + 8 + 15

⇒ s - a + s - b + s - c = 15 + 15

⇒ s - a + s - b + s - c = 30

⇒ s + s + s - a - b - c = 30

⇒ 3s = 30 + ( a + b + c )

⇒ ( 3s / 2 ) = ( 30 / 2 ) + ( a + b + c ) / 2 - - [ Dividing each term by 2 ]

⇒ 3s / 2 = 15 + s - - [ ∵ s = ( a + b + c ) / 2 ]

⇒ 3s = ( 15 + s ) * 2

⇒ 3s = 30 + 2s

⇒ 3s - 2s = 30

⇒ s = 30 cm

∴ The semi perimeter of the triangle is 30 cm.

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Verification:

We have,

s = 30 cm

( s - a ) = 7 cm

( s - b ) = 8 cm

( s - c ) = 15 cm

Now,

( s - a ) = 7

⇒ 30 - a = 7

⇒ 30 - 7 = a

⇒ a = 23

Now,

( s - b ) = 8

⇒ 30 - b = 8

⇒ 30 - 8 = b

⇒ b = 22

Now,

( s - c ) = 15

⇒ 30 - c = 15

⇒ 30 - 15 = c

⇒ c = 15

Now, we know that,

Semi perimeter of triangle = ( Sum of sides ) / 2

⇒ s = ( a + b + c ) / 2

⇒ 30 = ( 23 + 22 + 15 ) / 2

⇒ 30 = ( 45 + 15 ) / 2

⇒ 30 = 60 ÷ 2

⇒ 30 = 30

∴ LHS = RHS

Hence verified!