The perimeter of a triangular piece of land is 120m it’s area is 600m sq. If one of its sides is 30m, find the other two sides.

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

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