Question

In an triangle the side are in the ratio 3: 4:5. Find the area
of the triangle if its perimeter is 60 m.​

Answer 1

Step-by-step explanation:

Let the 1st side be 3x

2nd side be 4x

3rd side be 5x

Now, it's perimeter is 60 m

so, 3x + 4x + 5x = 60

12x = 60

x = 5 m

So the 1st side is 15m

2nd side is 20m

3rd side is 25m

Hope it helps you

Thank you

Answer 2

Before, finding the answer. Let's find out on how we can find the answer.

• To find the Area, we must first find the sides.
• So, to find that we must add all the ratio's together.
• Now, we are supposed to divide the Perimeter by the total ratios.

$\sf x = \dfrac{Perimeter }{Total \: Ratio}$

• At last, we must multiply the Ratio's with x to find the side.
• Now, for finding the Area. We must use Heron's formula which is :

-----

• Where, we have to find the Semi Perimeter by the formula of :

$\sf \dfrac{a + b + c}{2}$

• And then :

$\sf \sqrt{s (s-a) (s-b)(s-c)}$

_____________________

Given :

• Ratio = 3:4:5
• Perimeter = 60 m

To find :

• area  of the triangle

Solution :

Total Ratio = 3 : 4 : 5

                  = 3 + 4 + 5

                  = 12

Let the sides be 3x, 4x and 5x.

x = Perimeter/Total Ratio

  = 60/12

  = 5

Side A = 3x

           = 3 × 5

           = 15 m

Side B = 4x

           = 4 × 5

           = 20 m

Side C = 5x

           = 5 × 5

           = 25 m

Hence, the lengths are 15m, 20m and 25 m.

Now,

Semi-Perimeter of Triangle = $\sf \dfrac{a + b + c}{2}$

                                              = $\sf \dfrac{15 + 20 + 25}{2}$

                                              = $\sf \dfrac{60}{2}$

                                              = 30

∴ Semi-Perimeter of Triangle is 30 m.

Area of Triangle = $\sf \sqrt{s (s-a) (s-b)(s-c)}$

                           = $\sf \sqrt{30 (30-15) (30-20)(30-25)}$

                           = $\sf \sqrt{30 \times (15) \times (10) \times (15)}$

                           = $\sf \sqrt{67500}$

∴ Area of Triangle is √67500 m².