# A rectangular parking lot is 50ft longer than it is wide. How do you determine the dimensions of the parking lot if it measures 250 ft diagonally?

##### 2 Answers

#### Explanation:

Let length be

Let width be

Given

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using Pythagoras

But

Divide both sides by 2 giving:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using the formula:

where

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check

length = 200 ft and width = 150 ft

#### Explanation:

If we let the width = x , then length = x + 50

( I recommend you draw a sketch )

There is now a right-angled triangle with 2 sides of x and

( x + 50 ) and hypotenuse = 250.Using Pythagoras' Theorem to obtain :

# x^2 + (x + 50 )^2 = 250^2 # (distribute the bracket )

# x^2 + x^2 + 100x + 2500 = 62500 # (collect 'like terms' and equate to 0 )

# 2x^2 +100x - 60000 = 0# ( divide equation by 2 ) :

#x^2 + 50x - 30000 = 0 # We now require 2 factors of - 30000 which multiply to - 30000

and add to + 50.( These are 200 and - 150)

[You should use the quadratic formula if not sure .]

equation now becomes (x + 200 )(x - 150 ) = 0

solving gives : x = - 200 or x = 150

x ≠ - 200 hence x = 150

so width = x = 150 and length = x + 50 =150 + 50 = 200