Answer:

Sure, here are the answers to your questions:

Q1: The sides of the triangle are in the ratio of 12:17:25, which means they can be written as 12x, 17x, and 25x (where x is a common factor). The perimeter of the triangle is given as 540cm, so we can write:

12x + 17x + 25x = 540

Simplifying this equation, we get:

54x = 540

x = 10

Substituting this value of x back into the side lengths, we get:

12x = 120cm

17x = 170cm

25x = 250cm

Now we can use Heron's formula to find the area of the triangle:

s = (120 + 170 + 250)/2 = 270

Area = √[s(s-a)(s-b)(s-c)] where a, b, and c are the sides of the triangle.

Area = √[270(270-120)(270-170)(270-250)]

Area = √[270*150*100*20]

Area = √[729000000]

Area = 27000 cm²

Therefore, the area of the triangle is 27000 cm².

Q2: We are given two sides of the triangle as 18cm and 10cm, and the perimeter is given as 42cm. Let the third side be x. Then we can write:

18 + 10 + x = 42

Simplifying this equation, we get:

x = 14

Now we can use Heron's formula to find the area of the triangle:

s = (18 + 10 + 14)/2 = 21

Area = √[s(s-a)(s-b)(s-c)] where a, b, and c are the sides of the triangle.

Area = √[21(21-18)(21-10)(21-14)]

Area = √[21*3*11*7]

Area = √[4851]

Area ≈ 69.7 cm²

Therefore, the area of the triangle is approximately 69.7 cm².

Hope that helps!

Step-by-step explanation:

1. ratio of sides of triangle is 12:17:25

sides of triangle is 12x,17x,25x

perimeter of triangle = sum of side

12x+17x+25x = 540

54x=540

x =540/54 =10

therefore sides are 120,170 and 250

2. perimeter of triangle = sum of three sides

third side is x

18+10+x = 42

28+x = 42

x = 42-28 = 14cm

Area = √[s(s-a)(s-b)(s-c)]

s=a+b+c / 2 = 42/2 = 21

A = √21(21-18)(21-10)(21-14)

A= √21×3×11×7= 21 √11 cm²

A= 69.64cm²