The height of a parallelogram is 18 centimeters less than its base. If the parallelogram has an area of 175 square centimeters, what is the height

Question

Algebra 1

Answer 1

 

Let        b = the base of the parallelogram

Let b - 18 = the height of the parallelogram ... 18 less than the base

 

The area of a parallelogram = base • height

 

   175 = b•(b - 18)

   175 = b² - 18b

   b² - 18b - 175 = 0

   (b - 25)(b + 7) = 0

 

   b - 25 = 0 ... b = 25

   b + 7 = 0 ... b = -7 ... discard ... the length cannot be negative

 

So the base is 25, and the height is 25 - 18, or 7

 

Answer 2

The formula for the area of a parallelogram is A=bh. We know that h = b - 18. So we can substitute in A = b(b -18). Distribute b through, and we get A = b^2-18b.

 

From here, we can plug in 175 for the area. 175 = b^2 - 18b. Move the 175 to the right to get the equation to equal 0 (so we can factor the trinomial), and we have 0 = b^2 - 18b - 175.

 

When we factor this, we get (b+7)(b-25)=0.

 

Using the zero product property, we know that either b+7 = 0 or b-25=0. Solving each of these for b gives b = -7 or b = 25. We can exclude b = -7 because we can't have a negative measurement. Therefore, b = 25.

 

To find the height, we subtract 18 from this, and that gives us 25-18 = 7.