The length of a rectangular garden is 3 yd more than twice its width. The perimeter of the garden is 30 yd What are the width and length of the garden?

Question

Savannah Anderson · Accepted Answer

The width of the rectangular garden is 4yd and the length is 11yd.

For this problem let's call the width #w#. Then the length which is "3 yd more than twice its width" would be #(2w + 3)#. The formula for the perimeter of a rectangle is: #p = 2w *+ 2l# Substituting the information provided gives: #30 = 2w + 2(2w + 3)# Expanding what is in parenthesis, combining like terms and then solving for #w# while keeping the equation balanced gives: #30 = 2w + 4w + 6# #30 = 6w + 6# #30 - 6 = 6w + 6 - 6# #24 = 6w# #24/6 = (6w)/6# #w = 4# Substituting the value of #w# into the relationship for length gives: #l = (2*4) + 3# #l = 8 + 3# #l = 11#

Isaiah Anthony · Answer

undefined Let's denote the width of the rectangular garden as 'w' yards. According to the given information, the length of the garden is 3 yards more than twice its width, which can be expressed as 2w + 3 yards.

The perimeter of a rectangle is given by the formula: P = 2(l + w), where 'l' is the length and 'w' is the width.

Given that the perimeter of the garden is 30 yards, we can write the equation as:

30 = 2(2w + 3 + w).

Solve this equation for 'w' to find the width of the garden.

30 = 2(3w + 3)

Now, distribute the 2:

30 = 6w + 6

Subtract 6 from both sides:

24 = 6w

Divide both sides by 6:

w = 4

So, the width of the garden is 4 yards.

Now, substitute 'w = 4' into the expression for the length of the garden:

l = 2w + 3

l = 2(4) + 3

l = 8 + 3

l = 11

So, the length of the garden is 11 yards.

Therefore, the width of the garden is 4 yards, and the length of the garden is 11 yards.

Jace Anderson · Answer

undefined Let the width of the garden be $ w $ yards.
Then, the length of the garden is $ 2w + 3 $ yards.
The perimeter of the garden is $ 2(w + 2w + 3) = 30 $ yards.
Solving for $ w $:
$$ 2(w + 2w + 3) = 30 $$
$$ 2(3w + 3) = 30 $$
$$ 6w + 6 = 30 $$
$$ 6w = 24 $$
$$ w = 4 $$
So, the width of the garden is $ 4 $ yards, and the length is $ 2(4) + 3 = 11 $ yards.