The diagonal of a rectangle is 13 meters. The length is 2 meters more than twice the width. What is the length?

1 Answer
Dec 21, 2016

Answer:

Length is #12# meters

Explanation:

We can use the Theorem of Pythagoras.

Let the width be #x#
The length is then #2x+2#

By Pythagoras' Theorem:

#x^2 + (2x+2)^2 = 13^2" "larr#square the binomial

#x^2 + 4x^2 + 8x +4 = 169" "larr# make it = 0

#5x^2 +8x +4-169 =0#

#5x^2 +8x -165 = 0#

Find factors of 5 and 165 which subtract to give 8
Note that #165 = 5 xx33#

#33-25 = 8#

#(x-5)(5x +33)=0" "# set each factor = 0

#x-5 = 0 " "rarr x = 5#

#5x+33=0" "rarr 5x = -33# Reject the negative value

If #x-5 " "rarr 2x+2 = 12#

We could also have guessed at this outcome using the
Pythagorean triples... 13 is a clue!

The common triples are:

#3:4:5" "and 5:12:13" "and " "7:24:25#

Note that #5 xx2+2 = 12" "larr# this fits what we want.

#5^2 +12^2 = 25+144 = 169#
#13^2 = 169#