The sum of the base and the height of a triangle is 21cm. Determine the maximum area of the triangle, in square centimeters.
Solution
Area of a triangle:½ (b)(h)
b: base measurement of the triangle, h: height measurement of the triangle.
b + h = 21 || b = 21 – h
21h – h^2 = 0
h^2 – 21h = 0
h^2 – 21h +110.25 – 110.25 = 0
h^2 – 21h +110.25 = 110.25
(h-10.5)^2 = 110.25
√(h-10.5)^2 = √110.25
h-10.5 = ± 10.5
h = 10.5 ± 10.5 , h = 10.5 + 10.5, h = 21 || h = 10.5 – 10.5, h = 0
h = 10.5 + 10.5, h = 21
Divide 21 by 2
b = 21 – (h), b = 21 – (10.5), b= 10.5
h = 10.5, b = 10.5
Now plug in these values to find the area of the triangle.
Therefore, the area of the triangle, is 55.125 cm2