the area of a trapezoid is 99 square centimeters. If the shorter base is 1 less than twice the height, and the longer base is double the shorter base, find the length of the longer base.
This is my equation that I've written: 99=1/2(2x-1) + (4x-2)*h, I then simplified it down to 99=(3x-1.5)*h. Can you tell me am i going in the right direction? And help me.
Thanks, Jabria
You're close, but you can express everything in terms of the height.
height: h
shorter base: 2h-1
longer base: 4h-2
so, now find h using
1/2 (2h-1 + 4h-2)h = 99
6h - 3 = 198
and so on
Yes, you are on the right track with your equation!
To find the length of the longer base, let's break down the information given:
1. The area of the trapezoid is 99 square centimeters.
2. The shorter base is 1 less than twice the height.
3. The longer base is double the shorter base.
Let's assign variables to the unknown values:
- Let x be the shorter base.
- Let h be the height.
Using the formula for the area of a trapezoid, we have:
Area = 1/2 * (sum of bases) * height
So, plugging in the given information, we get:
99 = 1/2 * (x + 2x - 1) * h
Simplifying this equation:
99 = 1/2 * (3x - 1) * h
Now, to continue solving for x (the longer base), let's isolate it in the equation. Divide both sides of the equation by h and then multiply both sides by 2 to remove the fraction:
99 = 1/2 * (3x - 1) * h
99 * 2 = (3x - 1) * h
198 = 3x - 1h
198 + 1 = 3x
199 = 3x
Now, divide both sides by 3 to solve for x:
199/3 = x
Therefore, the length of the shorter base (x) is approximately 66.33 centimeters.
Since the longer base is double the shorter base, we can find it by multiplying x by 2:
Longer base = 2 * 66.33 = approximately 132.67 centimeters.
So, the length of the longer base is approximately 132.67 centimeters.
Please note that these results are approximate due to the decimal values involved.