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givi [52]
2 years ago
12

The width of the rectangle is 1/4 the length. The perimeter of the rectangle is 225 feet. Find the length and width of the recta

ngle.
Mathematics
1 answer:
Mariana [72]2 years ago
6 0

Answer:

The length and width of rectangle are 90 feet and 22.5 feet.

Step-by-step explanation:

Let the,

  • \purple\star Length of rectangle be : x
  • \purple\star Breadth of rectangle be : x/4

Now, according to the question substituting all the given values in the formula to find the value of x :

\longrightarrow{\pmb{\sf{P = 2(L  +  W)}}}

  • > P = perimeter
  • > L = length
  • > W = width

\longrightarrow{\sf{P = 2(L  +  W)}}

\longrightarrow{\sf{225= 2 \bigg(x +   \dfrac{x}{4}  \bigg)}}

\longrightarrow{\sf{225= 2 \bigg(\dfrac{4x + x}{4}  \bigg)}}

\longrightarrow{\sf{225= 2 \bigg(\dfrac{5x}{4}  \bigg)}}

\longrightarrow{\sf{225= 2 \times \dfrac{5x}{4}}}

\longrightarrow{\sf{225= \dfrac{2 \times 5x}{4}}}

\longrightarrow{\sf{225= \dfrac{10x}{4}}}

\longrightarrow{\sf{10x = 225 \times 4}}

\longrightarrow{\sf{10x  = 900}}

\longrightarrow{\sf{x  = \dfrac{900}{10}}}

\longrightarrow{\sf{\underline{\underline{x  = 90}}}}

Hence, the value of x is 90.

Now, we know the value of x. So, calculating the length and width of rectangle :

  • \pink\star Length = 90 feet
  • \pink\star Width = 90×1/4 = 22.5 feet

\rule{300}{2.5}

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