A triangle has a base length of (2x +16) mm. find the height of The triangle if its area is ( 3x^2+ 8x- 3) mm^2 ?

The area of a triangle is given by the formula:

Area = 1/2 * base * height

Given that the base length is (2x + 16) mm and the area is (3x^2 + 8x - 3) mm^2, we can set up the equation:

(3x^2 + 8x - 3) = 1/2 * (2x + 16) * height

Now, we can solve for the height:

(3x^2 + 8x - 3) = (x + 8) * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x^2 + 8x - 3 = 2x * height + 16 * height
3x

Area of triangle = ½ x base x height
(3x^2 8x- 3) = ½ (2x +16) x height
(3x^2 8x- 3) = ( x^2 +8x ) x height
(3x^2 8x- 3) = x^2 +8x x height =
3x^2 8x- 3 =x^2 +8x x height
3x^2 8x- 3 = x^2 +8x
3x^2 8x- 3 = x^2 + 8x
3x^2 8x- 3 - x^2 - 8x = 0
3x^2 -x^2 8x -8x - 3 = 0
2x^2 -3 = 0
2x2 =3
x^2 =3/2
x^2 =1.5
Square root both sides we have
X= √1.5
X= 1.224
Therefore, height = x^2 +8x
= (1.224) ^2 +8(1.224)
= 1.499 +9.792
=11.291mm