The height of a triangle is 6 m more than twice the length of the base. The area of the triangle is 18 m. Find the height of the
1 answer:
Answer:
height = 12 m
Step-by-step explanation:
let the base be x then height = 2x + 6 ( 6 more than twice the base )
The area (A) of a triangle is calculated as
A = bh ( b is the base and h the height ), thus
A = x(2x + 6)
Given A = 18, then
x(2x + 6) = 18
Multiply both sides by 2 to clear the fraction
x(2x + 6) = 36 ← distribute left side
2x² + 6x = 36 ( divide all terms by 2 )
x² + 3x = 18 ( subtract 18 from both sides )
x² + 3x - 18 = 0 ← in standard form
(x + 6)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 3 = 0 ⇒ x = 3
But x > 0 ⇒ x = 3
Thus height = 2x + 6 = 2(3) + 6 = 6 + 6 = 12
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9514 1404 393
Answer:
maximum height of 17.07 feet about 10.67 feet from the club
returns to the ground 21.33 feet away
Step-by-step explanation:
A graphing calculator can answer these questions easily.
The vertex of the quadratic ax²+bx+c is given by x=-b/(2a). For this quadratic function, the highest point is found at ...
x = -(3.2)/(2(-0.15)) = 32/3 = 10 2/3 . . . . feet horizontally from the club
The maximum height is the function value at that point.
h(10 2/3) = (-0.15(10 2/3) +3.2)(10 2/3) = 1.6(10 2/3) = 17 1/15
The ball reaches a maximum height of 17 1/15 feet at a horizontal distance of 10 2/3 feet from the club. The ball's flight is symmetrical about the peak, so it returns to the ground about 21 1/3 feet away.
