Question

The base of the isosceles triangle is parallel to x-axis and has both end-points on the parabola y=x(10−x) and its vertex belongs to the x-axis. Find area of the triangle if the length of its base is 8.

Answer 1

Answer:

36

Step-by-step explanation:

We must determine the x and y intercepts of the parabola:

When y=0, x=0 or x=10

WE know that the point of the triangle base is x and x+8. We can substitute this into the parabola equation because the endpoints are on the parabola.

f(x+8)$=-(x^2+16x+64)+10x+80$

f(x+8)$=-x^2-6x+16$

f(x)=f(x+8)

$-x^2+10x=-x^2-6x+16$

solve for x

$16x=16$

$x=1$

Therefore the heigh is f(1):

$=-1^2+10=9$

The area of the triangle is 1/2 base x height:

$=(1/2)\cdot{8}\cdot{9}=36$