Question

the perimeter of triangular garden is 900cm and its sides are in the ratio 3:5:4.find the area of the triangular garden using herons formula

Answer 1

Let the common multiple be x
3x+5x+4x=900
12x=900
x=75
3x=75*3=225
5x=75*5=375
4x=75*4=300

Area,
S=225+375+300/2
=450
Area=√450(450-225)(450-375)(450-300)
=√450*225*75*150
=5*3*2*5*3*5*3*5
=33750cm

Answer 2

Answer:

The area of the triangular garden using Heron's Formula is 33750cm²

Step-by-step explanation:

We have a triangular garden whose perimeter is 900cm and its sides are in the ratio of 3:5:4 we have to calculate the area of the triangle by using Heron's Formula

Step 1 of 4

Since the sides are in ratio so there must be one common factor, let that common factor be x then

3x + 5x + 4x = 900

⇒12x = 900

⇒x = 75

Step 2 of 4

Then the sides of triangle a, b, c becomes

a = 3*75 = 225

b = 5*75 = 375

c = 4*75 = 300

Step 3 of 4

For applying Heron's Formula we need to calculate the value of s which can be calculated as

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

⇒s = $\frac{225+375+300}{2}$

⇒s =75

Step 4 of 4

Now by applying Heron's Formula we get

Area of Triangular Garden = $\sqrt{s(s-a)(s-b)(s-c)$

                                             = $\sqrt{450(450-225)(450-375)(450-300)$

                                              =$\sqrt{450*225*75*150$

                                              =33750cm²

Hence the area of triangular garden using Heron's formula is 33750cm²