A rectangle has a side whose length is 5 and a diagonal whose length is √74. What is the area of the rectangle?

Hint: the other side is 7.

To find the area of a rectangle, we need to know the lengths of both sides. In this case, we are given one side with a length of 5, but we need to find the length of the other side.

Let's use the Pythagorean Theorem to find the length of the other side. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, let's say the length of the other side is x. Applying the Pythagorean Theorem, we have:

x^2 + 5^2 = (√74)^2

Simplifying, we get:

x^2 + 25 = 74

Subtracting 25 from both sides:

x^2 = 49

Taking the square root of both sides:

x = √49

Which means x can be either 7 or -7. However, the length of a side cannot be negative, so x = 7.

Now that we have both side lengths, we can find the area of the rectangle by multiplying the two sides together:

Area = length * width
= 5 * 7
= 35

Therefore, the area of the rectangle is 35 square units.