MathFind n if the area of the triangle determined by the graph of the function f = nx + n - 4 and the x,y axis where is A = n/2 .

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The area of the triangle whose sides are the graph of f(x) and x, y axis is the area of a right angle triangle: half-product of cathetus.

The cathetus of the triangle are x and y axis, where the values of x and y are the intercepts of the graph with x and y axis.

A = x*y/2

We'll calculate x intercept of f(x). We'll put y = 0.

f(x) = 0

nx+n-4 = 0

We'll isolate x to the left side:

nx = 4 - n

x = (4-n)/n

We'll calculate y intercept of f(x). We'll put x = 0.

f(0) = n - 4

y = n - 4

Now, we'll calculate the area:

A = (4-n)*(n-4)/2n

We know, from enunciation, that A=n/2.

n/2 = -(n-4)^2/2n

We'll cross multiply:

2n^2 = -2(n-4)^2

We'll divide by 2:

n^2 = (n-4)^2

We'll subtract (n-4)^2 both sides:

n^2 - (n-4)^2 = 0

We'll expand the square:

n^2 - n^2 + 8n - 16  = 0

We'll eliminate like terms:

8n - 16 = 0

We'll add 16

8n = 16

n = 2

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