Calculate Rectangle Area: Given BC=5 and Perimeter=40

The perimeter of the rectangle equals:

$P=AB+BC+CD+DA$

Since we know that BC equals 5 and in a rectangle opposite sides are equal to each other, we get:

$40=AB+5+CD+5$

$40=10+AB+CD$

Since AB equals CD we can write the equation as follows:

$40=2AB+10$

Let's move 10 to the other side and change the sign accordingly:

$40-10=2AB$

$30=2AB$

Let's divide both sides by 2:

$15=AB$

Now we know the length and width of the rectangle and can calculate its area:

$15\times5=75$