I am studying for exams and need help with one of my review problems.
A paraellogram has sides of lenghts 12 cm and 20 cm. If the area of the paraellogram is 600 sq cm then find the length of the shorter height of the parallelogram.
To find the length of the shorter height of the parallelogram, we first need to calculate its base length.
In a parallelogram, the opposite sides are equal in length. Therefore, if one side is 12 cm, the opposite side is also 12 cm. Similarly, if one side is 20 cm, the opposite side is also 20 cm.
The area of a parallelogram is given by the formula: Area = base × height.
We are given that the area is 600 sq cm. Let's denote the base as "b" and the height as "h."
So, we have the equation: 600 = b × h.
Since the base length is either 12 cm or 20 cm, we need to consider both possibilities.
1. If the base length is 12 cm, we can substitute it into our equation: 600 = 12 × h.
Solving for h, we divide both sides by 12: h = 600 / 12 = 50 cm.
2. If the base length is 20 cm, we substitute it into our equation: 600 = 20 × h.
Solving for h, we divide both sides by 20: h = 600 / 20 = 30 cm.
Therefore, the two possible lengths for the shorter height of the parallelogram are 50 cm and 30 cm.