Given that the perimeter of a rectangle
equals 72 centimeters and the ratio between the lengths of two of its sides is five to
four, determine its area.
Let’s consider the rectangle as shown
with length 𝑥 centimeters and width 𝑦 centimeters. We are told that its perimeter is equal
to 72 centimeters. And the perimeter of a rectangle is the
distance around the outside. As the opposite sides of a rectangle
are parallel and equal in length, we have the equation 𝑥 plus 𝑦 plus 𝑥 plus 𝑦 is equal
to 72. Grouping or collecting like terms, this
equation simplifies to two 𝑥 plus two 𝑦 is equal to 72.
We can divide both sides of the
equation by two, giving us 𝑥 plus 𝑦 is equal to 36. We are also told in the question that
the ratio between the lengths of the two sides is five to four. Therefore, 𝑥 and 𝑦 are in the ratio
five to four. We now know the sum of the two
quantities and the ratio between them.
We can calculate one part of the ratio
by dividing the sum of the quantities by the number of parts. In this case, one part or one share is
equal to 36 divided by nine. This is equal to four. Our next step is to multiply each of
the parts by four. Five multiplied by four is equal to
20. And four multiplied by four is equal to
16. This means that the lengths 𝑥 and 𝑦
are 20 centimeters and 16 centimeters, respectively.
We were asked to determine the area of
the rectangle. We do this by multiplying the length by
the width. Two multiplied by 16 is equal to
32. Therefore, 20 multiplied by 16 is
320. The area of the rectangle is 320 square