Quadratic questions

[Guest]

I need help with these 3 quadratic type questions.

1.The sum of the base and the heaight of a triangle is 21 cm. Determine the maximum area of the triangle, in square centimetres.



2.Reena wants to fence part of her front yard for a flower bed. What is the maximum area she cn enclose if she has 30 m of fencing?


3.a)Find the minimum product of two numbers whose difference is 17.
b)What are the two numbers?


-thanks for the help,
Anna

 

[Denis]

I need help with these 3 quadratic type questions.
1.The sum of the base and the heaight of a triangle is 21 cm. Determine the maximum area of the triangle, in square centimetres. Anna

A square gives max area; triangle needs to be half a 10.5 by 10.5 square;
(10.5)^2 / 2 = 55 1/8 = max area

Can you follow this:
b = base; then height = 21 - b
area = b(21 - b) / 2 = (21b - b^2) / 2
set that = 0 and take derivative:
b^2 - 21b = 0
2b - 21 = 0
2b = 21
b = 10.5