Problema Solution
The area of a field shaped like a right triangle is 750 yards squared. One leg of the field is fenced with wood costing $5/yd. the remainder of the perimeter of the field is fenced with steel costing $10/yd. The perimeter of the field is 150 yards. The total cost of the fencing is $1200.
What is the length of the leg fenced with wood?
What is the length of each leg fenced with steel?
Answer provided by our tutors
let 'a', 'b' and 'c' represent the sides of the field, with 'c' the longest side (the hypotenuse)
area of a triangle = (1/2)base * height
for the field, then, we have:
750 = (1/2)ab
1500 = ab
perimeter = sum of all three sides:
150 = a + b + c
let 'x' represent the length of the field fenced with $5/yd wood, then '150-x' represents the length of the field fenced with $10/yd steel
1200 = 5x + 10(150-x)
solving for 'x' we have x=60
150-60 = 90
so 60 yards was fenced with wood and that represents one side of the field, then the other two sides of the field were fenced with 90 yards of steel
we assume b=60, then we have:
90 = a + c
1500=a60
a = 25
90 = 25 + c
c = 90-25 = 65
a check that this is consistent with a right triangle:
65^2 = 4225
60^2 + 25^2 = 4225
the length of the legs fenced with steel are 25 and 65 yards
60 yards are fenced with wood