Answer:

Step-by-step EXPLANATION:

(6) Let the sides of the triangle be 13x,14x and 15x.

Therefore, 13x+14x+15x=84

42x=84

x=2

Hence, sides of the triangle are 26 cm , 28 cm & 30 cm.

Area of the triangle =√s*(s-a)*(s-b)*(s-c).

[Heron's Formula]

s=a+b+c/2=26+28+30/2= 84/2=42.

a=26cm

Area=√42*(42-26)*(42-28)*(42-30).

b=28 cm

Area=√42* 16*14*12. c=30 cm

Area=√42*2688

Area=√112896

Area=336 cm²

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(7) Let the sides be 13x, 14x and 15x

Perimeter = Sum of all sides

84 = 13x + 14x + 15x

42x = 84

x = 2

So, the sides are a = 26 cm, b = 28 cm and c = 30 cm

s = p/2 = 84/2 = 42 cm

Area = √s(s - a)(s - b)(s - c)

= √42(42 - 26)(42 - 28)(42 - 30)

= √42*16*14*12

= 4√14*14*36

= 4*14*6

= 336 cm^2

So, area of triangle = 336 cm^2

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(8) Semi perimeter = s

s =( AB +BC + AC)/2

s = (17 + 8 + 15)/2 = 40/2 = 20cm

By Heron's formula, area of triangle ABC,

Area = √s(s-a)(s-b)(s-c)

= √20 (20 - 17) (20 - 8) (20 - 15)

= √20 (3 x 12 x 5)

= √20 x 180

= √3600 = 60cm²

Again area of triangle = 1/2 base x height\

60 = 1/2 x 17 x h

h = 120/17

h = 7.05cm

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(9) Let The THIRD Side Be xcm.

Now Perimeter = 12+12+x

24+x = 30

x = 6

Now Find The Area Using Herons Formula

Semiperimeter = 30/2 = 15

Sq Root(15(15-12)(15-12)(15-6) ) = Sq Root(15*3*3*9) = Sq Root(1215) = 34.85 cm^2

So Area is 34.85cm^2

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the perimeter of isosceles triangle = 32cm

p of isosceles triangle = 2 * equal side + base

let length of equal side be 3x and base be 2x

then

2 * 3x + 2x = 32 cm

6x + 2x = 32cm

8x = 32 cm

x= 4 cm

length of equal side = 3*4= 12cm

length of base = 2*4=8cm

area of isosceles triangle=b*1/4*√4a2-b2

= 8*1/4√4*144-64

=2√512

=2*22.62

= 45.25cm2

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Hope it helps

:)