Write an expression in simplest form to represent the area of the triangle.
Width is x^2-8x+16/4x^2
Length is 2x^2-10x/x^2-9x+20
To find the area of the triangle, use the formula for the area of a triangle:
Area = 0.5 * (Width) * (Length)
Area = 0.5 * ((x^2-8x+16)/(4x^2)) * ((2x^2-10x)/(x^2-9x+20))
Simplify the expression:
Area = 0.5 * ((x-4)/(4x)) * (2x(x-5)/((x-5)(x-4)))
Area = 0.5 * (1/4) * 2
Area = 0.25
Therefore, the area of the triangle is 0.25.
Are you sure
My apologies for the mistake. Let's correct the solution:
Area = 0.5 * ((x^2 - 8x + 16) / (4x^2)) * ((2x^2 - 10x) / (x^2 - 9x + 20))
We need to factorize the expressions in the numerators and denominators before simplifying:
Area = 0.5 * ((x - 4)(x - 4) / (4x)(x)) * (2x(x - 5) / (x - 5)(x - 4))
Now, simplify further:
Area = 0.5 * ((x - 4)(x - 4) / 4x^2) * (2x(x - 5) / (x - 5)(x - 4))
Area = ((x - 4)(x - 4) / 8x^2) * (2x(x - 5) / (x - 5)(x - 4))
Now simplify the expression:
Area = 2(x - 4) / 8x
Finally, simplify by cancelling a 2 from the numerator and the denominator:
Area = (x - 4) / 4x
Therefore, the expression in simplest form to represent the area of the triangle is (x - 4) / 4x.