the area of a parallelogram is 507 square cm, and its height is three times its base. find the base and the height.
Uuhjj
13 and 39
To find the base and height of the parallelogram, we need to use the formula for calculating the area of a parallelogram. The formula is:
Area = base * height
Given that the area of the parallelogram is 507 square cm, we can set up the equation:
507 = base * height
It is also given that the height is three times the base, so we can substitute the height with 3 times the base:
507 = base * (3 * base)
Now, let's simplify the equation:
507 = 3 * base^2
Next, we need to isolate the base by dividing both sides of the equation by 3:
base^2 = 507 / 3
base^2 = 169
To solve for the base, we need to take the square root of both sides:
base = √169
base = 13
So, the base of the parallelogram is 13 cm.
To find the height, we can substitute the value of the base into the equation:
height = 3 * base
height = 3 * 13
height = 39
Hence, the height of the parallelogram is 39 cm.
h = 3b
h * b = 507
Substitute 3b for h in second equation and solve for b. Insert that value into the first equation and solve for h. Check by inserting both values into the second equation.