# a triangle has a base area of (2 -x) cm and a height of (2x+6) cm.?

What is the maximum area of the triangle. What value of x will produce the maximum area?

Update:

PLEASE HELP

### 2 Answers

Relevance

- lenpol7Lv 71 year ago
A = (0.5)(2-x)(2x + 6)

2A = 4x + 12 - 2x^2 - 6x

2A = -2x^2 - 2x + 12

A = -x^2 - x + 6

At Max (Area)

dA/dx = -2x - 2 = 0

2x = -2

x = -1

Hence

A = (0.5)(2 -- - 1)(2(-1) + 6)

A = ).5)(3)(4)

A = (0.5)(12)

A = 6 (Max Area) at x = -1

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