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