Question

47. Maximizing Area. The sum of the base and the

height of a triangle is 20 cm. Find the dimensions
for which the area is a maximum.

Answer 1

Below

Explanation:

Area = 1/2 base * h and base + h = 20 ( then base = 20-h)

Area = 1/2 (20-h) *h

-1/2 h^2 + 10h <=== you could graph this to see the maximum or:

max occurs at (for a quadratic) h = -b/2a = -10/(2 *-1/2) = 10

then base = 20 -10 = 10 also

base = 10 height = 10