The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perimeter would be 62 inches. What is the width and length of the rectangle?

Question

Jayden Jackson · Accepted Answer

Length is #21# and width is #7# Ill use #l# for length and #w# for width First it is given that #l=3w# New length and breadth is #l+2# and #w+1# respectively Also new perimeter is #62# So, #l+2+l+2+w+1+w+1=62# or, #2l+2w=56# #l+w=28# Now we have two relations between #l# and #w# Substitute first value of #l# in the second equation We get, #3w+w=28# #4w=28# #w=7# Putting this value of #w# in one of the equations, #l=3*7# #l=21# So length is #21# and width is #7#

Mason Adams · Answer

undefined Let's denote the width of the rectangle as $ w $ inches. Then, the length of the rectangle would be $ 3w $ inches according to the given information.

When the length is increased by 2 inches and the width by 1 inch, the new length becomes $ 3w + 2 $ inches and the new width becomes $ w + 1 $ inches.

The perimeter of a rectangle is given by the formula:

$$ \text{Perimeter} = 2 \times (\text{length} + \text{width}) $$

According to the problem, the new perimeter is 62 inches:

$$ 62 = 2 \times ((3w + 2) + (w + 1)) $$

Solve this equation for $ w $ to find the width of the rectangle.

$$ 62 = 2 \times (4w + 3) $$
$$ 62 = 8w + 6 $$
$$ 8w = 62 - 6 $$
$$ 8w = 56 $$
$$ w = \frac{56}{8} $$
$$ w = 7 $$

So, the width of the rectangle is 7 inches.

Now, substitute this value of $ w $ back into the expression for the length to find its value:

$$ \text{Length} = 3w $$
$$ \text{Length} = 3 \times 7 $$
$$ \text{Length} = 21 $$

So, the length of the rectangle is 21 inches.