Rhizanntaguilingidn
Answered

Makakuha ng maliwanag na mga sagot sa iyong mga tanong sa IDNStudy.com. Ang aming platform ay idinisenyo upang magbigay ng mabilis at eksaktong sagot sa lahat ng iyong mga tanong.

The length of a rectangle is 8 more than twice it's width.If the area of the rectangle is 24 sq. meters,find its dimensions​

Sagot :

KAntoineDoixidn

✏️AREA

==============================

[tex] \large \bold{\blue{PROBLEM:}} [/tex]The length of a rectangle is 8 more than twice it's width.If the area of the rectangle is 24 sq. meters, find its dimensions.

[tex] \large \bold{\blue{SOLUTION:}} [/tex] Represent 'l' and 'w' as the length and the width respectively. Make equations on the given statements and use the formula on how to find the area of a rectangle.

  • [tex] \begin{cases} l = 2w + 8 \\ 24 = l \cdot w \end{cases} \: \begin{align} \red{(eq. \: 1)} \\ \red{(eq. \: 2)} \end{align} [/tex]

» Substitute the value of 'l' in terms of 'w' into the second equation.

  • [tex] \begin{cases} l = 2w + 8 \\ 24 = (2w + 8) \cdot w \end{cases} [/tex]

  • [tex] \begin{cases} l = 2w + 8 \\ 24 = 2w^2 + 8w \end{cases} [/tex]

  • [tex] \begin{cases} l = 2w + 8 \\ 2w^2 + 8w - 24 = 0 \end{cases} [/tex]

» Solve the second equation using the quadratic formula. Make sure that the solution has the positive result.

  • [tex] w = \frac{-8 \pm \sqrt{8^2 - 4(2)(-24)}}{2(2)} \\ [/tex]

  • [tex] w = \frac{-8 \pm \sqrt{64 + 192}}{4} \\ [/tex]

  • [tex] w = \frac{-8 \pm \sqrt{256}}{4} \\ [/tex]

  • [tex] w = \frac{-8 \pm 16}{4} \\ [/tex]

  • [tex] w = \frac{-8 + 16}{4} \\ [/tex]

  • [tex] w = \frac{8}{4} \\ [/tex]

  • [tex] w = 2 [/tex]

  • [tex] \begin{cases} l = 2w + 8 \\ w = 2 \end{cases} [/tex]

» After finding the length of the width, substitute it to the first equation to find the length.

  • [tex] \begin{cases} l = 2(2) + 8 \\ w = 2\end{cases} [/tex]

  • [tex] \begin{cases} l = 4 + 8 \\ w = 2 \end{cases} [/tex]

  • [tex] \begin{cases} l = 12 \\ w = 2 \end{cases} [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{l = 12 \: meters, \: w = 2 \: meters}}} [/tex]

==============================

#CarryOnLearning

(ノ^_^)ノ

[tex] \huge{\bold{ Answer: }}[/tex]

[tex] \bold{length = 12m} \\ \bold{width = 2m}[/tex]

Solution:

We know that :

  • Area of rectangle = length × width

Given :

  • Area of the rectangle = 24 m[tex]^{2}[/tex]
  • The length of a rectangle is 8 more than twice it's width.

_________________________________

Let x be the width of rectangle

Therefore :

[tex] Length = 2x + 8 \\ x(2x + 8) = 24 \\ 2x^{2} + 8x = 24 \\ 2x^{2} + 8x - 24 = 0 \\ x^{2} + 4x - 12 = 0 \\ (x+6)(x-2)=0 \\ (x+6)=0 \: or \: (x=2)=0 \\ x=-6 \: or \: x=2[/tex]

_________________________________

Hence width = 2m

Length = 2 × 2 + 8 = 4 + 8 = 12m

_________________________________

(/^_^)/

Ang iyong aktibong pakikilahok ay mahalaga sa amin. Magpatuloy sa pagtatanong at pagbibigay ng mga sagot. Sama-sama tayong lumikha ng isang masiglang komunidad ng pagkatuto. Ang IDNStudy.com ay laging nandito upang tumulong sa iyo. Bumalik ka palagi para sa mga sagot sa iyong mga katanungan.