The length of a rectangle is one less than 3 times the width. The area is 70 m sq. What
are the length and width?

l= 10 , w=7

Step-by-step explanation:

If the length of a rectangle is 11 m less than 3 times the width, then we can come up with this equivalency:

l = 3w - 11

where l stands for length and w stands for width. Now we plug in the equivalency into the equation for the area of a rectangle:

A = lw

A = (3w - 11)w

70 = (3w - 11)w

70 = 3w2 - 11w

Then solve for w by completing the square. Now, in order to complete the square for this, we need to find a completion that fits 3w2 - 11w +  ?  and completes the base factoring of (√(3)w -  ? )2. The only one that fits the second question mark so that it can work out to the first is (11√3)/6, and when we work it into the first question mark, the first question mark becomes 121/12. Essentially, what we have for completing the square is:

70 + 121/12 = 3w2 - 11w + 121/12

80.08333 = (√(3)w - (11√3)/6)(√(3)w - (11√3)/6)

80.08333 = (√(3)w - (11√3)/6)2

8.94893 = √(3)w - (11√3)/6

Solving for w, we get:

12.124 = √(3)w

w = 7

Since we know that the length is 11 m less than 3 times the width, we can plug w into the first equation to find l:

l = 3w - 11

l = 3(7) - 11

l = 21 - 11

l = 10

And if we want to check, lw = (10)(7) = 70.