Answer:
The other two sides are 40m and 50m
Step-by-step explanation:
Let the sides be a , b and c
adding all together will give the perimeter
a + b + c = 120, now since one of the sides, let’s say a is 30
this means b + c = 120-a = 120-30 = 90
b + c = 90 •••••••••• (i)
We can use Heron’s formula to find the area of the triangle
Firstly, s = (a + b + c)/2 = 120/2 = 60
Using the formula;
A = √s(s-a)(s-b)(s-c)
We already have a as 30 and a as 60;
so we have;
600 = √60(60-30)(60-b)(60-c)
600 = √(60)(30)(60-b)(60-c)
Squaring both sides we have
360000 = 1800(60-b)(60-c)
divide both sides by 1800
200 = (60-b)(60-c) ••••(ii)
from the first equation we know that b + c = 90
so b = 90-c , we substitute this into ii
200 = (60-(90-c))(60-c)
200 = (60-90+c)(60-c)
200 = (c-30)(60-c)
200 = 60c-c^2-1800+30c
200 = -c^2 -1800 + 90c
we can rearrange this as;
c^2 -90c + 2000 = 0
c^2-50c-40c+ 2000 = 0
c(c-50)-40(c-50) = 0
(c-40)(c-50) = 0
Thus c = 40 or 50
Since sum of both b and c is 90
This means b also is also 40 or 50
from b = 90-40 or b = 90-50
So we can confidently say the other two sides are 40 m and 50 m
