# Simple Equation in One Variable ( + some Geometry)

• May 4th 2013, 11:55 PM
MoniMini
Simple Equation in One Variable ( + some Geometry)
Hi there guys!
I've a problem solving this Linear Equations question.

Quote:

ABCD is a rectangle with sides 36cm and 90cm. P is a point on BC, which is one of the longer sides, such that PA = 2PD.
The length of PB is-
a) 80cm b)18cm c)72cm d)64cm
Alright, I drew the Rough Sketch and all... but I don't know how to proceed after that.
I took the areas of PAD and (PAB + CDP) and the 2 sides of the equation but this way
all the values get cancelled out and you get 1=1. I couldn't really figure out how
Pythagorean Theorem would solve the problem either.

Any advice will be highly appreciated

Thanks
~MoniMini
• May 5th 2013, 01:17 AM
ManosG
Re: Simple Equation in One Variable ( + some Geometry)
$\displaystyle If \quad PB = x, \quad then \quad PC = 90-x. \quad So, \quad PA = \sqrt{(36)^2 + x^2} \quad and \quad PD = \sqrt{(36)^2 + (90 - x)^2}. \quad Use \quad also \quad the \quad fact \quad PA = 2PD \quad and \quad you \quad will \quad find \quad x = PB$