I need help on this math problem.

Question

The width of a certain painting is 5cm less than twice the length. The length of the diagonal distance across the painting is 107cm. Find the length and width. Round your answer to 2 decimal places.

Substitute:
diagonal distance: 107cm
length: L
width: 2L-5

Is the substitutes correct?
Should I use the pythagoras method?
Can someone put me in the right track please so I can work out the problem?

please help and thank you

Answer 1

yes
yes

L^2 + (2L-5)^2 = 107^2
L^2 + 4L^2 - 20L + 25 = 11449
L = 49.84

Answer 2

the next step is:

5L^2-20L=11424

right?

Answer 3

Almost. Set the equation to zero to solve:

5L^2-20L-11424 = 0

then use the quadratic formula to get L.