SOLUTION: A triangle has a height of 2x and a base of 7 - 4x.
a) what is the maximum area of the triangle?
b) what value of x gives the maximum area?
Algebra.Com
Question 1048460: A triangle has a height of 2x and a base of 7 - 4x.
a) what is the maximum area of the triangle?
b) what value of x gives the maximum area?
Found 2 solutions by rothauserc, ewatrrr:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Area of triangle(A) = (1/2) * base * height
:
A = (1/2) * (7-4x) * (2x) = 7x - 4x^2
:
we want the first derivative, which is
:
7 -8x
:
set the first derivative = 0 and solve for x
:
7 -8x = 0
:
x = 7/8
:
note that the equation for the Area is a parabola that curves downward,
:
therefore the value of x is a maximum
:
************************************************************
x = 7/8
:
max Area = 7(7/8) - 4(7/8)^2 = 392/64 - 196/64 = 196/64 = 49/16
:
************************************************************
:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
A triangle has a height of 2x and a base of 7 - 4x.
A = (1/2)(7-4x)2x
A= - 4x^2 + 7x = -4(x - 7/8))^2 + 4(49/64) |completing the square
a) what is the maximum area of the triangle? 49/16
b) what value of x gives the maximum area? 7/8
RELATED QUESTIONS
a)A triangle has a base of (4-x) cm and height of (2x+3) cm , what is the maximum area of (answered by richard1234)
Triangle KLM has a base of 3x and a height of 4x. What is the area of triangle KLM in... (answered by solver91311)
a triangle has a base of x+6, and a height of 2x+3. what is the area of the... (answered by ReadingBoosters)
triangle a has a base of 12 and a height of 18. triangle b has a base of 16. what is the... (answered by solver91311)
What equation best represents the area of the triangle? The triangle has a height of x+2 (answered by Fombitz,Sir226)
A triangle has an area of 64 yd
and a base of 8, what is the height of the... (answered by richard1234)
The area of a triangle is 84 and the base is 7.What is the height of the triangle
(answered by jim_thompson5910)
What is the maximum area of a triangle having 15cm as the sum of its base and height ?... (answered by scott8148)
What is the maximum area of a triangle having 15 cm as the sum of its base and height ? (answered by macston)