What are the dimensions of the triangle

Question

Nita is building a fenced triangular chicken pen. The base will be 10 yards less than the height. The total are must be 28 square yards. Find the new dimensions of the chicken pen

 

Answer 1

A = (1/2)·b·h

• A = Area = 28 yd2
• b = base = h-10
• h = height

 

A = (1/2)·b·h

28 = (1/2)(h-10)h

56 = h² - 10h

0 = h² - 10h - 56

0 = (h-14)(h+4)

 

h = 14 and -4.  Since you can't have a negative height, h = 14 yd,  The base is b = h-10 = 14 - 10 = 4 yd.  Check:

 

A = (1/2)·b·h

28= (1/2)(4)(14)

28 = 28

Check!