Question

á Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area​

Answer 1

Answer:

Ratio = 12:17:25

Let the sides be 12x , 17x , 25x  respectively.

12x + 17x + 25x = 540

⇒ 54x = 540

⇒ x = 540/54

⇒ x = 10

∴ The sides are 120cm , 170cm , 250cm .

Step-by-step explanation:

Answer 2

→Question: Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area​.

↔Solution:

→Given: Sides of triangle in the ratio=12:17:25

           :  Perimeter of the triangle      =540cm

→To find:

            :Area of the triangle

Now,

Area of Triangle=√s(s-a)(s-b)(s-c)       (Heron's Formula)

Here,      

• s=semi perimeter
• a,b,c are sides of the triangle

Perimeter=540cm

Semi Perimeter=540÷2

Semi Perimeter=270cm

Sides in the ratio=12:17:25

so, 12x,17x,25x       (x is any number)

Perimeter=540cm

a+b+c=540cm              (perimeter=sum of all sides)

12x+17x+25x=540

54x=540

x=540÷54

∴x=10

• 12x=12×10=120cm
• 17x=17×10=170cm
• 25x=25×10=250cm

Now,Area of Triangle=√s(s-a)(s-b)(s-c)

We have the values of a,b,c

So,let's substitute and find the area.

⇔√s(s-a)(s-b)(s-c)

⇔√270(270-120)(270-170)(270-250)

⇔√270×150×100×20

⇔√27×15×2×10^5      

⇔√27×30×10^5

⇔√27×3×10^6         (the o of 30 is transposed to 10^5)

⇔√81×10^6

⇔√9²×10^6

⇔9×(10^6)1/2

⇔9×10³

⇔9000

∴Area of the triangle=9000cm²