The area of a field shaped like a right triangle is 750yd^2. 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 150yd. The total cost of the fencing is $1200.

A - What is the length of the leg fenced with wood?

B - What is the length of the leg fenced with steel?

Assume that

a and b = the two legs of the right triangle.

c = the hypotenuse.

The area of the right triangle is 750 yd², therefore

(1/2) * a*b = 750

ab = 1500 (1)

The perimeter is 150yd, therefore

a + b + c = 150 (2)

Let the side fenced with wood be a, at $5/yd. Sides b and c are fenced with steel at $10/y. The total cost is $1200, therefore

5a + 10b + 10c = 1200

or

a + 2b + 2c = 240 (3)

From (2), obtain

c = 150 - a - b (4)

Substitute (4) into (3)

a + 2b + 2 (150 - a - b) = 240

-a + 300 = 240

a = 60

From (1), obtain

60b = 1500

b = 25

From (4), obtain

c = 150 - 60 - 25 = 65

Answer:

A. The length of the leg fenced with wood is 60 yd.

B. The length of the leg fenced with steel is 25 yd.