Algebra word math problem

Question

The area of a rectangle is 273 square centimeters. If the perimeter is 68 centimeters, find the length and width of the rectangle.

Answer 1

The Area of a rectangle is given by A = w x l. and perimeter is P = 2 x (l+w). Since you know those two values, you can solve for the length l and width w like so

273 = w x l

273/l = w

68 = 2 x (l+w)

34 = l + w

34 - l = w

Setting the equal

273/l = 34 - l. solving for l

273 = 34 l - l^2

l^2 - 34L + 273 = 0. Using the quadratic formula. you get

L = 13 or L = 21

Thus solving for w

34 - L = w

w = 34 - 13 = 21

w = 34 - 21 = 13.

So the dimensions of the rectangle is 13 and 21. which can either be length or width.

Answer 2

A = lw

w = A/l

P = 2(l + w)

P/2 = l + w

w = P/2 - l

A/l = P/2 - l

273/l = 68/2 - l

273/l = 34 - l

273 = l(34 - l)

273 = 34l - l2

l2 - 34l + 273 = 0

(l - 13)(l - 21) = 0

l - 13 = 0

l = 13

l - 21 = 0

l = 21

We now have two measurements which multiply together to give us our area. The length is the longer.

Length = 21 cm

Width = 13 cm