Question

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.

Answer 1

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