Question

a piece of wire of length 240cm is bent into the shape as shown in the diagram.Find the value of x and y which A is maximum,hence find the maximum area

Answer 1

can u find the area of that figure,in terms of x and y?

Answer 2

give me a few minutes

Answer 3

i think its
24xy+100x^2

Answer 4

also wire length=perimeter = 13x+13x+24x+y+y=240
now can u find y in terms of x,from this?

Answer 5

@shendelzare_3011 part a easy one
240=2y+24x+23x+13x
this can be done give me few minutes for part b

Answer 6

how 100x^2,isn't it 60 x^2 ?
1/2*5*24

Answer 7

y=(240-50x)/2,y=160/3 when x=8/3
max area is 3840

Answer 8

how did u get x=8/3?

Answer 9

i got it..

Answer 10

Firstly y in terms of x...
y = 120 - 25x

next u split the diagram into 2 right angle triangles + a rectangle

Area of rectangle = 24xy << substitute y in u get 2880x-660x^2

now to find the perpendicular height of the right angle triangle
u know that the base of each triangle is 12x
so squareroot of (13x^2 - 12x^2) = 5x therefore,
Area of triangle = 1/2 times 5x tmes 12x
u got 2 triangles so it is 60x^2

Answer 11

then add the area of the 2 triangles + the area of the rectangle which is
2880x - 660x^2 + 60x^2

Answer 12

Diferentiate 2880x - 540x^2 to and let it equals 0

Answer 13

\[\frac{ dA }{ dx } = 2880 - 1080x = 0\]

Answer 14

Solving for x gives u x= 2.666666667
\[2\frac{ 2 }{ 3 }\]

Answer 15

then u know that y = 120 -25x << substitute ur x value in here and get your y value
Then to get ur area.. just substitute ur x value into ur area equation
( A = 2880x-520x^2 )

Answer 16

get it..?

Answer 17

not really
but,i will try to figure it out
thanks :D

Answer 18

no problem :) if u dont understand , feel free to leave a message here

Answer 19

thanx :D
i get it now