Problema Solution
The area of a field shaped like a right triangle is 600 square yards. The ,legs of the field are fenced with steel costing $10/m, while the hypotenuse is fenced with aluminum at $20/m. The perimeter of the field is 120m. The total cost of then fencing is $1700. Give the lengths of the three sides of the field.
Answer provided by our tutors
area of a triangle = (1/2)b*h where 'b' and 'h' are legs of the triangle expressed in meters
we express the area in square meters:
600yd^2 * 9ft^2/yd^2 * ft^2 * 0.092903m^2/ft^2 = 501.6762m^2
let 'c' represent the hypotenuse of the triangle in meters and we have these equations:
perimeter: 120 = b + h + c
area: 501.6762 = (1/2)bh
cost: 1700 = 10(b+h) + 20c
solving this system:
120 = b + h + c
501.6762 = (1/2)bh
1700 = 10(b+h) + 20c
we have c = 50, b = 20.1 and h = 49.88
or c = 50, b = 49.88 and h = 20.1 since it is not specified which leg is longer
the three sides of the field measure approximately 20, 50 and 50 meters