Linear Equation Word Problem

Question

The perimeter of a triangular plot of land is 2400 ft. The longest side is 200 ft. less than twice the shortest. The middle side is 200ft. less than the longest side. Find the lengths of the three sides of the triangular plot. 

Answer 1

P = 2400

define the 3 sides as follows

t = longest side

s = shortest side

m = middle side

 

We are told that

t = 2s - 200

This can be rewritten as s = (1/2)(t+200)  

m = t - 200

 

If t + s + m = 2400

t + (1/2)(t+200) + (t-200) = 2400

t + t/2 + 100 + t - 200 = 2400

(5/2)t -100 = 2400

(5/2)t = 2500

t = 1000 = longest side

s = (1/2) (t+200) = 600 = shortest side

m = t-200 = 800 = middle side

 

Just to check

1000 + 600 + 800 = 2400