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## 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

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# 1 Answer

*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 + 3WEquation 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 + 3W

^{2}= 232 [We now have an equation with only variable, W, to solve for]3W

^{2}+ 5W - 232 = 0 [A quadratic equation!]**Step 4**- Solve for W. Use the quadratic formula.

W = -(b/2a) ± (1/2a)√(b

^{2}-4ac) where a=3, b=5, c= -232 from our quadratic equationW = -(5/6) ± (1/6) √(5

^{2}-(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!