One side of a rectangle is 60 cm longer than ten times another side. Find the length of the sides, given that the area of the rectangle is 720 cm2. What are both sides?

Answer 1

Hi Tuscanee! Let me know if the video helps.

Let's call the two side lengths of the rectangle w and h (for width and height).

We first have to translate the word problem into algebra:

One side is 60 cm longer than 10 times another side.

is --> = (equals)

longer --> + (add)

times --> * (multiply)

Let's say "one side" is w and "another side" is h. When we translate, we get our Equation 1:

w = 60 + 10h

Then, we're told the area of the rectangle is 720 cm². (Let's ignore the cm for now, since everything is in cm or cm² -- we don't have to worry about it!)

A = 720

What's the formula for the area of a rectangle? Area equals width times height, or:

A = wh

If area is width times height and we're told the area is 720, then width times height for our rectangle must be 720! That's our Equation 2:

wh = 720

We know from our first equation that w = 60 + 10h. Let's replace w in Equation 2 with 60 + 10h (from Equation 1):

(60+10h)h = 720

Now we can solve this equation for h, since this just becomes a quadratic equation (see the video for more details). After that, we can plug that value of h into Equation 2, which helps us solve for the value of w. Don't forget to check your answer by replacing w and h in Equation 1 and seeing if that makes sense!