The formula for the area of a parallelogram is A = bh. The area of the parallelogram in the illustration is 300 square centimeters. If its base is three times its height, how long is the base?
Let's assume the height of the parallelogram is "h" centimeters.
According to the given information, the base of the parallelogram is three times its height. So, the base can be represented as 3h centimeters.
The formula for the area of a parallelogram is A = bh, where A represents the area, b represents the base, and h represents the height.
Given that the area of the parallelogram is 300 square centimeters, we can substitute the values into the formula:
300 = (3h)h
To solve for h, let's simplify the equation further:
300 = 3h^2
Now, divide both sides of the equation by 3 to isolate h^2:
100 = h^2
To find the value of h, we take the square root of both sides:
√100 = √h^2
Simplifying,
10 = h
Therefore, the height of the parallelogram is 10 centimeters.
Since the base is three times the height, we can calculate the base as:
Base = 3h = 3 * 10 = 30 centimeters.
Hence, the base of the parallelogram is 30 centimeters.
To solve this problem, we can follow these steps:
Step 1: Understand the problem:
We are given that the area of a parallelogram is 300 square centimeters. The base is three times the height, and we need to find the length of the base.
Step 2: Recall the formula for the area of a parallelogram:
The formula for the area of a parallelogram is A = base × height.
Step 3: Set up the equation using the given information:
Let the height of the parallelogram be represented by h. According to the problem, the base is three times the height, so the base would be 3h.
Therefore, the equation for the area of the parallelogram can be written as: A = (3h) × h, which simplifies to A = 3h^2.
Step 4: Substitute the given area into the equation:
We are given that the area is 300 square centimeters, so we can replace A with 300: 300 = 3h^2.
Step 5: Solve for h:
To find the value of h, we need to isolate it on one side of the equation.
Divide both sides of the equation by 3: 300/3 = h^2.
Simplifying further, we have: 100 = h^2.
Step 6: Take the square root of both sides:
Taking the square root, we find that the possible values for h are ±10. However, since height cannot be negative, we take the positive value, so h = 10.
Step 7: Calculate the base:
We know that the base is three times the height, so we multiply the height h by 3: base = 3 × 10 = 30.
Therefore, the length of the base is 30 centimeters.
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b = 3h or b/3 = h
A = 300 = bh = b*b/3 = b^2/3
300 = b^2/3
Solve for b.