The equal sides of an isosceles trapezoid each measure 5, and its altitude measures 4. If the area of the trapezoid is 48, find the lengths of its bases.

hah, I will guess 3,4,5 triangle at each end

base = top + 6

4(base + top)/2 = 48
base + top = 24
2 top + 6 = 24
top = 9
base = 15

Well, let's see... An isosceles trapezoid, huh? Fancy! So, we know that it has two equal sides measuring 5 and an altitude of 4. And, the area is 48. Interesting puzzle, none other than an Acrobatic Trapezoid! Now, to find the lengths of the bases, we can use a little math magic.

The area of a trapezoid is calculated by the formula: area = (sum of bases) × (altitude) ÷ 2.

We're given that the area is 48 and the altitude is 4. The sum of the bases, which we need to find, will be multiplied by the altitude and divided by 2.

So, let's substitute the known values into the formula:

48 = (sum of bases) × 4 ÷ 2.

Now, to isolate the sum of the bases, we can divide both sides of the equation by 4 and then multiply by 2:

48 ÷ 4 × 2 = sum of bases.

Simplifying this, we get:

12 × 2 = sum of bases,

24 = sum of bases.

Since an isosceles trapezoid has two equal sides, the sum of the bases will be twice the length of either base. So, let's divide the sum of the bases by 2 to find the length of each base:

24 ÷ 2 = 12.

Therefore, each base of the trapezoid measures 12 units.

Voila! The lengths of the bases of this mysterious trapezoid are 12 units each. Now it's time for this juggling act to continue!

To find the lengths of the bases of the isosceles trapezoid, we can use the formula for the area of a trapezoid.

The formula for the area of a trapezoid is given by:

Area = (base1 + base2) * height / 2

Let's denote the length of one of the equal sides of the trapezoid as x. Since the equal sides are given to be 5, we have:

x = 5

The altitude of the trapezoid is given to be 4, so we have:

height = 4

Finally, the area of the trapezoid is given as 48:

48 = (base1 + base2) * 4 / 2

Dividing both sides by 4, we get:

12 = (base1 + base2) / 2

Multiplying both sides by 2, we have:

24 = base1 + base2

Since the trapezoid is isosceles, the lengths of the bases are equal. Let's denote the length of a base as b. So we have:

base1 = base2 = b

Substituting this into the equation, we get:

24 = b + b

Combining like terms, we have:

24 = 2b

Dividing both sides by 2, we get:

12 = b

Therefore, the lengths of the bases of the isosceles trapezoid are both equal to 12.

To find the lengths of the bases of the isosceles trapezoid, we can use the formula for the area of a trapezoid:

Area = (1/2) * (sum of bases) * height

In this case, the area is given as 48, and the height is given as 4. Let's substitute these values into the formula:

48 = (1/2) * (sum of bases) * 4

Now, let's solve for the sum of the bases:

48 = 2 * (sum of bases)

(sum of bases) = 48 / 2

(sum of bases) = 24

Since the trapezoid is isosceles, the two bases have the same length. Let's denote the length of each base as x. Therefore, we have:

2x = 24

Dividing both sides of the equation by 2:

x = 24 / 2

x = 12

Hence, the lengths of the bases of the isosceles trapezoid are 12 units each.