a trapezoid has an area of 36 meters squared and altitude of 2 meters. its two bases in meters have ratio of 4:5 the bases are ___.
The area of the trapezoid is 36 m^2.
Well, well, well, looks like we've got ourselves a trapezoid puzzle! Let's put on our thinking caps, shall we?
So, we know the area of the trapezoid is 36 square meters, and the altitude is 2 meters. That's a great start!
Now, let's use the formula for the area of a trapezoid: Area = (1/2) × (sum of bases) × altitude. Since we already know the area and altitude, all we need to figure out is the sum of the bases.
Let the bases be 4x and 5x, where x is some number. We need their sum to be the height of hilarity... I mean, 36 divided by 2, which is 18. So, setting up our equation:
4x + 5x = 18
Combine like terms:
9x = 18
Divide both sides by 9:
x = 2
Now we can find the actual lengths of the bases by substituting our x back into the equation:
Base 1 = 4x = 4(2) = 8 meters
Base 2 = 5x = 5(2) = 10 meters
So, my friend, the bases of this tricky trapezoid are 8 meters and 10 meters.
I hope that brought a smile to your face, even if it's just a mathematical one!
To find the lengths of the two bases of the trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) × (sum of the bases) × altitude.
In this case, we know that the area is 36 square meters, and the altitude is 2 meters. Let's denote the shorter base as 4x and the longer base as 5x (since the ratio of the bases is 4:5).
Now we can solve the equation:
36 = (1/2) × (4x + 5x) × 2.
First, let's simplify the equation:
36 = (1/2) × 9x × 2.
Now, let's solve for x:
36 = 9x.
Divide both sides by 9:
x = 36/9.
x = 4.
Since we found the value of x to be 4, we can substitute this back into our expressions for the bases:
Shorter base = 4x = 4 * 4 = 16 meters.
Longer base = 5x = 5 * 4 = 20 meters.
Therefore, the two bases of the trapezoid are 16 meters and 20 meters.
(b+B)/2 * 2 = 36
b+B = 36
4x+5x=36
x=4
The bases are 16 and 20