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Elena-2011 [213]
2 years ago
12

the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width

Mathematics
2 answers:
egoroff_w [7]2 years ago
4 0

Answer:

  • Length and width of rectangle is 24 and 8 inches

Step-by-step explanation:

<u>Given:</u>

  • Length of rectangle is three times the width
  • Perimeter of rectangle is 64 Inches

<u>To Find:</u>

  • Length and Width

<u>Solution:</u>

Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:

Perimeter of rectangle = 2(L + B)

→ 64 = 2(3x + x)

→ 64 = 2(4x)

→ 64/2 = 4x

→ 32 = 4x

→ 32/4 = x

→ 8 = x

Hence,

  • Length of the rectangle = 3x = 3(8) = 24 inches

  • Width of the rectangle = x = 8 inches
Snowcat [4.5K]2 years ago
4 0

Answer:

  • Length = 24 inches

  • Width = 8 inches

⠀

Step-by-step explanation :

⠀

As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .

⠀

Now, According to the Question :

⠀

{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}

⠀

{\longrightarrow \qquad { {\sf{2 (3 x  + x )= 64 }}}}

⠀

{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}

⠀

{\longrightarrow \qquad { {\sf{8x= 64 }}}}

⠀

{\longrightarrow \qquad { {\sf{ x =  \dfrac{64}{8}  }}}}

⠀

{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar

⠀

Therefore,

  • The width of the rectangle is 8 inches .

⠀

Now, We are to find the length of the rectangle:

{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x  }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}

⠀

{\longrightarrow \qquad{ \underline{  \boxed{ \frak{\pmb{Length = 24}}}}}} \:  \:  \bigstar

⠀

Therefore,

  • The length of the rectangle is 24 inches .

⠀

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