Question

Use the given area to find the height and base of the triangle. base = 2x+5, height = x and area = 84?

word problem

Answer 1

Substitute the expressions into the Area equation and solve for 'x'.
`h = 8` ; `b = 21`

Explanation:

From the equation for the area of a triangle:
`A = 1/2 xx b xx h`

`84 = 1/2 xx (2x + 5) xx x`

`84 = 1/2 xx (2x^2 + 5x)` ; `84 = x^2 + 5/2x`

`x^2 + 5/2x - 84 = 0`

`x = (-b "+/-"sqrt((b^2 - 4ac)))/(2a)`

`x = (-5/2 "+/-"sqrt(((5/2)^2 - 4*1*-84)))/(2*1)`

`x = (-5/2 "+/-"sqrt(25/4 + 336))/2`

`x = (-5/2 "+/-"18.5)/2`

`x = 8`

`x = -10.25` ONLY the positive value is realistic for the physical problem.

`h = x = 8` ; `b = 2x + 5 = 21`