Question

The length of a rectangular deck is 3 times its width. If the deck’s perimeter is 32 feet, what is the deck’s area?

Answer 1

Given :

• Length of a rectangular deck is 3 times it's width.

• Perimeter of the rectangular deck = 32 feet

To find :

• Area of the deck

Concept :

Here, we have to find the area of the deck. So, firstly we need the value of the dimensions of the deck. In order to find the value the dimensions firstly we will assume them according the conditions given in the question. Then by using the formula of periemter of rectangle we will get the value of the dimensions of the deck.

Formula to find perimeter of rectangle :-

• Perimeter of rectangle = 2(l + b)

Formula to find the area of the rectangle :-

• Area of rectangle = l × b

where,

• l denotes the length of the rectangle

• b denotes the breadth of the rectangle

Solution :

Let us assume the breadth of the deck as x feet and length as 3 times it's width, i.e. 3x feet.

→ Perimeter of deck = 2(l + b)

→ Substituting the given :-

→ 32 = 2(3x + x)

→ 32 ÷ 2 = 3x + x

→ 16 = 4x

→ 16 ÷ 4 = x

→ 4 = x

→ The value of x = 4

Substituting the value of x in the dimensions of the deck :-

→ Length = 3x = 3 × 4 = 12 feet

→ Breadth = x = 4 feet

Therefore, the dimensions of the deck are 12 feet and 4 feet.

Now, calculating the area of the deck :-

→ Area of the deck = l × b

→ Substituting the given values :-

→ Area of the deck = 12 × 4

→ Area of the deck = 48

Therefore, the area of deck = 48 square feet.