The area of a rectangle is 42m^2 and the length of the rectangle is 11m less than three times the width. Find the dimensions of the rectangle

Question

The area of a rectangle is 42m^2 and the length of the rectangle is 11m less than three times the width. Find the dimensions of the rectangle

Answer 1

Hi Dani,

Recall that Area=length*width.

Since the length = 3*width-11, we can substitute that in for the length in the above equation to remove a variable.

So we get: 42=(3w-11)*w, which expands to 42=3w²-11w.

Subtract both sides by 42: 0=3w²-11w-42

Plug in 3, 11, and 42 into the quadratic formula as a, b, and c, respectively to solve for x (in this case, w).

Answer 2

Area of a rectangle is 42=lw.

The length, l= 3w-11

 

plug in the eqn 2 in the first eqn.

 

42= (3w-11)w

3w² -11w -42= 0

w²-11w -126= 0.          Drop/slip 3 and multiply (42x3=126)

(w+7)(w - 18)=0.            Factor

(3w+ 7)(w -6)=0.         Bring the 3 back and divide

The only solution that will make sense is w= 6m

 

Plug into l= 3(6)-11

l=7m

The dimensions are, the length is 7 m and the width is 6m.