Final answer:
The height of a parallelogram can be found by solving the equation 'Area = base × height' given the area is 175 square centimeters and the height is 18 centimeters less than the base. The base 'b' and the height 'b - 18' form a quadratic equation that can be solved to find 'b', after which subtracting 18 will give the height.
Step-by-step explanation:
The question is asking to find the height of a parallelogram given its area and a relationship between the base and the height. The area of a parallelogram is found using the formula Area = base × height. According to the given information, we know that the area is 175 square centimeters. The relationship between the base and the height of the parallelogram is such that the height is 18 centimeters less than the base. Therefore, we can denote the base as 'b' and the height as 'b - 18'. Plugging these into the formula for the area we get 175 = b × (b - 18).
To solve for 'b', we can set up and solve a quadratic equation. After finding the value of 'b', we can calculate the height by subtracting 18 centimeters from our value for 'b'. Let's go through the steps:
- 175 = b × (b - 18).
- Distribute the 'b' on the right side of the equation: 175 = b^2 - 18b.
- Rearrange to form a quadratic equation: b^2 - 18b - 175 = 0.
- Solve the quadratic equation using the quadratic formula or factorization (if possible).
- Substitute the positive value of 'b' back into 'b - 18' to find the height.
After solving the quadratic equation, we would get the value of 'b' and accordingly the value of 'b - 18' which is the height of the parallelogram in centimeters.