SOLUTION: if the sum of the base and the height of a triangle is 16 cm, what are the dimensions for which the area is a maximum?

Algebra ->  Triangles -> SOLUTION: if the sum of the base and the height of a triangle is 16 cm, what are the dimensions for which the area is a maximum?       Log On


   

Question 346239: if the sum of the base and the height of a triangle is 16 cm, what are the dimensions for which the area is a maximum?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.b%2Bh=16
2.A=%281%2F2%29bh
From eq. 1,
b=16-h
Substitute into eq. 2,
A=%281%2F2%29%2816-h%29h
A=%281%2F2%29%2816h-h%5E2%29
A=-%281%2F2%29h%5E2%2B8h
Convert to vertex form to find the maximum of A, A=a%28x-h%29%5E2%2Bk where (h,k) is the vertex.
A=-%281%2F2%29h%5E2%2B8h
A=-%281%2F2%29%28h%5E2-16h%29
A=-%281%2F2%29%28h%5E2-16h%2B64%29%2B64%2F2
A=-%281%2F2%29%28h-8%29%5E2%2B32
.
.
.

.
.
.
The vertex is (8,32).
The coefficient of the h%5E2 term is negative so the value at the vertex is a maximum.
Amax=32cm^2
highlight%28h=8%29cm
From eq. 1,
b%2B8=16
highlight%28b=8%29cm