Question

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 rectangle.

Answer 1

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

Step-by-step 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 + (x)/(4) \bigg)}}`

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

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

`\longrightarrow{\sf{225= 2 * (5x)/(4)}}`

`\longrightarrow{\sf{225= (2 * 5x)/(4)}}`

`\longrightarrow{\sf{225= (10x)/(4)}}`

`\longrightarrow{\sf{10x = 225 * 4}}`

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

`\longrightarrow{\sf{x = (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}`