Answered

Sir Noriel designed a rectangular garden. In his garden, the length is (x-8) meters and the width is (x-4) meters. If the area is of the garden is 107 square meters, what is the measure of its length and width?


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✒️Problem Solving

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[tex]\underline{\mathbb{PROBLEM }:}[/tex]

  • Sir Noriel designed a rectangular garden. In his garden, the length is (x-8) meters and the width is (x-4) meters. If the area is of the garden is 107 square meters, what is the measure of its length and width?

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[tex]\underline\pink{\mathbb{ANSWER }:}[/tex]

[tex]\large \ \: \begin{array}{|c|} \hline \\ \sf \: The \: garden \: has \: a \: length \: of \\ \sf \: 9 m \: and \: width \: of \: 13m. \\ \ \\ \hline\end{array}[/tex]

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[tex]\underline\blue{\mathbb{SOLUTION \: \& \: STEP - BY -STEP}:}[/tex]

Step 1: Understand the problem and find the measure of the length and width of Sir Noriel's rectangular garden.

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*In step 2, we will commonly use a working equation (WE) since we deal with polynomial equations.

Step 2: Devise a plan, We will use variables and a working equation. You can also use other methods or heuristics.

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*For step 3, you just need to apply all the basic concepts that you have learned on manipulating equations particularly the polynomial equations. Aside from that, make sure that you consider first the positive roots especially if the word problem involves real-life situations.

Step 3:Carry out the plan, Since (x-8) meters is measure of the length and (x-4) meters is the measure of the width, then the working equation is:

  • (x-8)(x-4) m² = 107 m²

We will now then remove first the units.

  • x ^ 2 - 12x + 32 = 107
  • x² 12x + 32 - 107 = 0
  • x²- 12x - 85 = 0
  • (x-17)(x+5)=0)
  • X2+5=0X2=-5

~Since we deal with real-life distances, choose the positive root. With that x = 17 Now let us proceed to the dimensions:

  • Length → (x - 8) = ((17) - 8) = 9 meters
  • Width → (x-4)= ((17)-4)= 13 meters

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Step 4: Look Back To check, let us see if the measures we obtained a while ago satisfy the working equation.

  • (x-8)(x-4) m² = 107 m²
  • (9)(13) * m ^ 2 = 107m
  • 107 m ^ 2 = 107²

Therefore, The garden has a length of 9 m and width of 13m.

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