The length and width of a rectangular poster are in a ratio of 4:5. The perimeter of the poster is 279 cm. Find the dimensions of the poster to the neasest tenth of a centimeter.

Answer 1

Hi Kylie,

To approach this problem, you are given some essential information.

Perimeter = 279 cm

Length-Width Ratio = 4:5

To solve this, you have to approach it with an equation. Now, picture a rectangle. You have two sides that are shorter and two sides that are longer. The shorter sides would have a ratio of 4x (this term comes from finding the standard unit of x and then multiplying that by 4 to find the side measurement of that side). The longer sides would have a ratio of 5x.

Now to find the perimeter, you add up all the sides. Well, we have 4x, 4x, 5x, 5x, so add 4x+4x+5x+5x = 18x. We know our perimeter to be 279 cm; we want to measure the length and width based on the ratio.

So 279 cm = 18x, divide 18 into both sides, and that should give you 15.5 cm = x {the unit measurement for the unknown).

Now we can determine the measurements for each side. We have already established that the two sides are shorter and have the same length.

4x & 4x, so 4(15.5 cm) & 4(15.5) gives us 2 sides with each 62 cm long.

For the longer sides, the ratio is 5x & 5x, so 5)15.5 cm) & 5(15.5 cm) gives us 2 sides with each 77.5 cm.

Now add up all the sides: 62 cm + 62 cm + 77.5 cm + 77.5 cm = 279 cm

Answer 2

Solve equations:

l/w = 4/5

2l + 2w = 279.

Round your answers.