Question

12. If (s - a ) = 7 cm, (s - b ) = 8 cm and (s - c ) = 15 cm. Find s.
pls urgent​

Answer 1

semi perimeter(s) of the triangle is 30

Question :

If (s - a) = 7 cm, (s - b) = 8 cm and (s - c) = 15cm. Find s.

Given :

(s - a ) = 7 cm,

( s - b ) = 8 cm,

(s - c ) = 15cm.

To Find :

Semi perimeter (s) of a triangle

solution :

We have the terms of side of triangle and the subtraction of semi perimeter.

Add the terms of semi perimeter and side of triangle,

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

$s - a + s - b + s - c = 30$

$(s + s + s) + (- a - b - c) = 30$

$3s = 30+ (a + b + c)$

Divide the given terms by 2 on both sides,

$( \frac{3s}{2} ) = ( \frac{30}{2}) + (\frac{a + b + c}{2} )$

Since,

s is the semiperimeter of the triangle, that is,

$s = (\frac{a + b + c}{2} )$

substitute the value of s in equation,

$\frac{3s}{2} = 15 + s$

$3s = 2(15 + s)$

$3s = 30 + 2s$

$3 s- 2 s= 30$

$s = 30$

Verification :

Substitute the value of (s) in the terms,

$(s - a) = 7 \\ (30 - a) = 7 \\ - a = 7 - 30 \\ - a = - 23 \\ a = 23$

$(s - b) = 8 \\ (30 - b) = 8 \\ - b = 8 - 30 \\ - b = - 22 \\ b = 22$

$(s - c) = 15 \\ (30 - c) = 15 \\ - c = 15 - 30 \\ - c = - 15 \\ c = 15$

Now Substitute the values of sides of triangle in heron's formula which says ,

The sum of three sides of triangle divided by 2 is equal to semi perimeter of the triangle

$s = \frac{(a + b + c)}{2}$

$s = \frac{(23 + 22 + 15)}{2} \\s = \frac{60}{2} \\ s = 30$

Hence verified.

Answer 2

Answer:

225 will be the answer to your question

Step-by-step explanation:

To find

Given

8 cm + 7 cm

= 15 cm

15 x 15

= 225 cm

S will 225 cm