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dem82 [27]
2 years ago
15

The length of a rectangle is 12 feet more than twice the width. If the area is 320 square feet, what is the length? What is the

width?
Mathematics
1 answer:
Softa [21]2 years ago
7 0

Answer:

  • Length of rectangle is 32 feet and width is 10 feet

Step-by-step explanation:

Given,

  • The length of a rectangle is 12 feet more than twice the width and area is 320 square feet

Let's assume, width of rectangle x feet and length of the Rectangle be 12 + 2x respectively. To Calculate the length and width of rectangle we'll use the formula of area of rectangle:

\\  \star \: { \underline{ \boxed { \pmb{ \sf{ \purple{Area  _{(rectangle)}= Length \times width}}}}}} \\ \\

Substituting the required values:

\dashrightarrow \sf \: \: \: \: (12 +2x) (x) = 320 \\

\dashrightarrow \sf \: \: \: \: 12x + 2x^2 = 320 \\

\dashrightarrow \sf \: \: \: \: 12x + 2x^2- 320 = 0 \\

\dashrightarrow \sf \: \: \: \: 2x^2 + 12 - 320 = 0 \\

\dashrightarrow \sf \: \: \: \: 2(x^2 + 6x - 160) = 0 \\

\dashrightarrow \sf \: \: \: \: 2(x^2 + 16x - 10x - 160) = 0 \\

\dashrightarrow \sf \: \: \: \: 2(x - 10)(x + 16) = 0 \\

\dashrightarrow \:  \:  \:  \:  \underline{  \boxed{ \purple{ \pmb{ \rm{  x = 10  \: or \: -16}}}}} \\

Hence,

  • Width of rectangle = x = 10 feet
  • Length of rectangle = 12 + 2x = 12 + 2(10) = 32 feet

~

\underline{\therefore{ \pmb { \frak{Length \:  and  \: width  \: of \:  rectangle  \: is   \: 32  \: and  \: 10  \:ft}}}}

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