The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 126 cm^2, what is the length of the diagonal?

1 Answer
Sep 10, 2015

sqrt(277)"cm" ~~ 16.64"cm"

Explanation:

If w is the width of the rectangle, then we are given that:

w(w+5) = 126

So we would like to find a pair of factors with product 126 which differ by 5 from one another.

126 = 2 * 3 * 3 * 7 = 14 * 9

So the width of the rectangle is 9"cm" and the length is 14"cm"

Alternative method

Instead of factoring in this way, we could take the equation:

w(w+5) = 126

rearrange it as w^2+5w-126 = 0

and solve using the quadratic formula to get:

w = (-5+-sqrt(5^2-(4xx1xx126)))/(2xx1)=(-5 +-sqrt(25+504))/2

=(-5+-sqrt(529))/2=(-5+-23)/2

that is w = -14 or w = 9

We are only interested in the positive width so w = 9, giving us the same result as the factoring.

Finding the diagnonal

Using Pythagoras theorem, the length of the diagonal in cm will be:

sqrt(9^2+14^2) = sqrt(81+196) = sqrt(277)

277 is prime, so this does not simplify any further.

Using a calculator find sqrt(277) ~~ 16.64