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

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

$\rule{300}{2.5}$