the length of a rectangle is 5m more than three times the width. The area is 232m2. Find the length and width of the rectangle

Question

I don't know how to solve it! Will someone please help me??

Answer 1

The length of a rectangle is 5m more than three times the width. The area is 232m2. Find the length and width of the rectangle.

 

Step 1 - What are the unknowns you're asked to find?

 

Find the length and width of the rectangle.

 

Let L= the length of the rectangle

Let W = its width

 

Step 2 - We have 2 unknowns (L and W), so we need two equations that relate the unknowns

 

Equation 1. the length of a rectangle is 5m more than three times the width:  L = 5 + 3W

Equation 2.  The area is 232m2:  Area = L*W = 232

 

Step 3 Substitution

 

Let's substitute 5+3W (from equation 1) in place of L in equation 2:

 

L*W = 232                      [Equation 2]

(5+3W)*W = 232            [Substituted 5+3W from equation 1 in place of L]

5W + 3W² = 232             [We now have an equation with only variable, W, to solve for]

 

3W² + 5W - 232 = 0        [A quadratic equation!]

 

Step 4 - Solve for W.  Use the quadratic formula.

 

W = -(b/2a) ± (1/2a)√(b²-4ac)   where a=3, b=5, c= -232 from our quadratic equation

 

W = -(5/6) ± (1/6) √(5²-(4)(3)(-232))

W = -(5/6) ± (1/6) √(2809)

W = -(5/6) ± (53/6)

 

W = 8, -58/6

 

We can't have a negative width (-58/6), so W = 8 meters

 

Step 5 - Solve for L

L = 5 + 3W             [Equation 1]

L = 5 + 3(8)            [Put in W=8]

L = 5 + 24

L = 29 meters

 

Step 6 Check

L*W = 232               [Equation 2]

(29)(8) = 232           [Put in L=29, W=8]

232=232                  CHECK!