Rose's garden is in the shape of a trapezoid. If the height of the trapezoid is 16m, one base is 20m and the area is 224m2, what is the length of the other base?
The area of a trapezoid is:
A= (1/2) h (b1 + b2)
...where h = height and b1, b2 are the bases.
Substitute what you know to solve for the unknown.
224 = (1/2)(16)(20 + x)
Hopefully, you can solve for x, which will be the other base.
224= 16(20+b2)
2x224= 320+b2/2x2
Since 320+b2 over 2 has to multiply by 2 to get rid of the denominator, 224(area), has to also multiply by 2.
448=320+b2/2
320 divided by 2 is 160
448 divided by 2 is 224 again.
224=160
b2=160
Second base equals 160
how-
Let's solve for x:
224 = (1/2)(16)(20 + x)
To get rid of the fraction, we can multiply both sides of the equation by 2:
448 = 16(20 + x)
Next, distribute the 16 on the right side:
448 = 320 + 16x
Now, let's isolate the variable x by subtracting 320 from both sides:
448 - 320 = 16x
128 = 16x
To solve for x, we divide both sides by 16:
128/16 = x
x = 8
Therefore, the length of the other base is 8m.
To solve for the length of the other base, we can start by rearranging the formula for the area of a trapezoid:
A = (1/2)h(b1 + b2)
Given that the height (h) is 16m, one base (b1) is 20m, and the area (A) is 224m^2, we can substitute these values into the formula:
224 = (1/2)(16)(20 + b2)
Simplifying the equation gives us:
224 = 8(20 + b2)
224 = 160 + 8b2
Subtracting 160 from both sides:
64 = 8b2
Dividing both sides by 8:
8 = b2
Therefore, the length of the other base (b2) is 8m.