The perimeter of a rectangle is 30 cm and its length is x cm. Find its area in terms of x. step by step explanation.​​

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1. Answer:

   Question:

   The perimeter of a rectangle is 30 cm and its length is x cm. Find its area in terms of x.

   To find:

   • Area in terms of x

   Given:

   • Perimeter = 30 cm

   • L = x

   Answer :

   To find area first we should know value of with.

   So first Let’s find width by using this formula:

   [tex]\blue{\boxed { \sf \underline {Perimeter=2(Length+Width)}}}[/tex]

   Insert Value of length and perimeter.

   30 = 2(x + width)

   [tex]: \implies \sf \dfrac{30}{2} = (x + width)[/tex]

   [tex]: \implies \sf{}x + width = \dfrac{ { \cancel{30}}^{ \: 15} }{ { \cancel{2}}^{ \: 1} }[/tex]

   [tex]: \implies \sf{}x + width = 15[/tex]

   [tex]: \implies \sf{} \star \underline{\underline{ width = 15 – x}} \star[/tex]

   Now Let’s find Area by using this formula

   [tex]\blue{\boxed { \sf \underline {Area=Length \times Width }}}[/tex]

   [tex]: \implies \sf{}Area = x \times (15 – x)[/tex]

   [tex]: \implies \sf{} \star \underline{\underline{ Area = 15x – {x}^{2} \: cm {}^{2} }} \star[/tex]

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