The length of a rectangle is 12 cm more than 6 times the width The perimeter is 108cm. How do you find length and width?

Question

The length of a rectangle is 12 cm more than 6 times the width  The perimeter is 108cm.  How do you find length and width?

Genesis Allen · Accepted Answer

Breadth = 6cm and length =48cm

In word problems where you want an equation, you need to define the unknown quantities first. It helps to choose the smaller quantity as #x# and write the other quantities in terms of #x#. Let the breadth of the rectangle be #x#. 6 times the breadth is #6x#. The length is 12cm longer than #6x# The length is #6x + 12# Write this: The perimeter of 108 cm is equal to the sum of its four sides, which are two lengths and two widths. #x + x + (6x +12) + (6x + 12) = 108" now solve for " x# #14x +24 = 108# #14x = 84# #x = 6# #x=6# is the breadth and #6x+12 = 36+12 = 48# is the length, Verify: 6 + 6 + 48 + 48 = 108 cm

Savannah Anderson · Answer

undefined To find the length and width of the rectangle, we can use the formulas for perimeter and the relationship between the length and width provided. Let's denote the width as $ w $ and the length as $ l $.

Given that the length is 12 cm more than 6 times the width, we can express this as $ l = 6w + 12 $.

The formula for the perimeter of a rectangle is $ P = 2l + 2w $. Substituting the expression for $ l $ into the formula for perimeter gives $ 108 = 2(6w + 12) + 2w $.

Now, we can solve for $ w $:

$$ 108 = 12w + 24 + 2w $$
$$ 108 = 14w + 24 $$
$$ 14w = 108 - 24 $$
$$ 14w = 84 $$
$$ w = \frac{84}{14} $$
$$ w = 6 $$

Now that we have the width, we can find the length using the expression we found earlier:

$$ l = 6w + 12 $$
$$ l = 6(6) + 12 $$
$$ l = 36 + 12 $$
$$ l = 48 $$

So, the width of the rectangle is 6 cm and the length is 48 cm.