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