# Inscribed rectangle in triangle

• Apr 24th 2007, 05:22 AM
AndrewK
Inscribed rectangle in triangle
Hi guys,

Need help with this one.

1) A recangle w/ a perimetrer of 15cm is inscribed in traingle ABC. A=(0,8) B=(6,0) C is unknown. Find the dimensions of the rectangle. Ill include a picture of the diagram so it will be more clear. :)

Thanks!!!
• Apr 24th 2007, 05:32 AM
malaygoel
Quote:

Originally Posted by AndrewK
Hi guys,

Need help with this one.

1) A recangle w/ a perimetrer of 15cm is inscribed in traingle ABC. A=(0,8) B=(6,0) C is unknown. Find the dimensions of the rectangle. Ill include a picture of the diagram so it will be more clear. :)

Thanks!!!

Is C required to be on X-axis?
• Apr 24th 2007, 06:17 AM
AndrewK
^ Yes it is malaygoel :)
• Apr 24th 2007, 08:36 AM
Jhevon
Quote:

Originally Posted by AndrewK
Hi guys,

Need help with this one.

1) A recangle w/ a perimetrer of 15cm is inscribed in traingle ABC. A=(0,8) B=(6,0) C is unknown. Find the dimensions of the rectangle. Ill include a picture of the diagram so it will be more clear. :)

Thanks!!!

first let's find the equation of the line.

what is the slope?

m = (y2 - y1)/(x2 - x1) = (8-0)/(0-6) = -4/3

using the point-slope form with m = -4/3 and (x1,y1) = (0,8), we get:
y - y1 = m(x - x1)
=> y - 8 = (-4/3)x
=> y = (-4/3)x + 8

now the rectangle goes up to the line y, that means the height of the rectangle will be given by the formula (-4/3)x + 8

now the length of the rectangle is just x. we are told that the perimeter is 15, which is the sum of all the sides, so

P = 15 = 2x + 2[(-4/3)x + 8]
=> 15 = 2x - (8/3)x + 16
=> 15 - 16 = -(2/3)x
=> -1 = -(2/3)x
=> x = 3/2

but y = (-4/3)x + 8 = (-4/3)(3/2) + 8 = 6

so the dimensions of the rectangle is length = 3/2, height = 6

let's check this to make sure:
P = 3/2 + 3/2 + 6 + 6 = .....drum roll please....= 15! Yay! ........that's 15, not 15 factorial:D

did you understand the process?