Question

The base of a rectangle is two thirds the length of its height. If the perimeter of the rectangle is 20 cm. What is the area?

Answer 1

For this case we have that by definition, the perimeter of a recatangle is given by:

$P = 2b + 2h$

Where:

b: It is the base of the rectangle

h: Is the height of the rectangle

According to the data of the statement we have:

$P = 20 \ cm\\b = \frac {2} {3} h$

Substituting we have:

$20 = 2 \frac {2} {3} h + 2h\\20 = \frac {4} {3} h + 2h\\20 = \frac {10} {3} h\\60 = 10h\\h = \frac {60} {10}\\h = 6$

Thus, the height of the rectangle is$6 \ cm$

$b = \frac {2} {3} (6) = 4 \ cm$

So the area is:

$A = b * h\\A = 4 * 6\\A = 24 \ cm ^ 2$

Answer:

$24 \ cm ^ 2$