Answer:
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.
