SOLUTION: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 120 cm2, what is the length of the diagonal?

Algebra ->  Rectangles -> SOLUTION: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 120 cm2, what is the length of the diagonal?      Log On


   

Question 1185479: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 120 cm2, what is the length of the diagonal?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Width 2L-4
Length L
120, the area

L%282L-4%29=120
---
L%28L-2%29=60---------------60=4%2A15=5%2A12=6%2A10

L%5E2-2L-60=0
L=%282%2B-+sqrt%284%2B4%2A60%29%29%2F2
L=%282%2B-+2sqrt%2861%29%29%2F2
highlight_green%28L=1%2Bsqrt%2861%29%29


%28L%29%5E2%2B%282L-4%29%5E2=d%5E2
d=sqrt%28L%5E2%2B4L%5E2-16L%2B16%29
highlight_green%28d=sqrt%285L%5E2-16L%2B16%29%29---------substitute here for L and evaluate d.

This was not rechecked yet.