Question

A triangular shaped lake-front lot has a perimeter of 1800 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. What are the lengths of all three sides?

Answer 1

500ft, 600ft and 700ft

Explanation:

If `x` is the shortest side then the other two would be `x+100` and `x+200`

All three sides add to make 1800 so we can write

`x+(x+100)+(x+200)=1800`

`3x+300=1800`

`3x=1500`

`x=500`

So the sides are 500, 600 & 700

Answer 2

`500,600" and "700" feet"`

Explanation:

`"let the shortest side "=x`

`"then the other 2 sides are "x+100" and "x+200`

`rArr"perimeter "=x+x+100+x+200=3x+300`

`"we are given perimeter "=1800`

`rArr3x+300=1800`

`"subtract 300 from both sides"`

`rArr3x=1500rArrx=1500/3=500`

`"sides are "x=500,x+100=600" and "x+200=700`