Find the area of the original parallelogram

[travishillier]

A Parallelogram has a base length of 12cm. In order to increse the area of the paralleogram by 54cm(squared), the length of the base is increased by 2cm and the height is incresed by 3cm . Find the area of the original parallelogram.

The solution requires me to use fully defined variables, formula(s), all steps shown using good math form and concluding statements with appropriate units .

Any help is greatly appreaciated ... PLMK what ui can do to help me ...

 

[HallsofIvy]

Heres the question ...

A Parallelogram has a base length of 12cm. In order to increse the area of the paralleogram by 54cm(squared), the length of the base is increased by 2cm and the height is incresed by 3cm . Find the area of the original parallelogram.

The solution requires me to use fully defined variables, formula(s), all steps shown using good math form and concluding statements with appropriate units .

Any help is greatly appreaciated ... PLMK what ui can do to help me ...

1. What in the world does this have to do with "linear and abstract algebra"?


2. Looks to me like homework and really should be in the homework section.


3. Let "h" be the original height. Since the original base length is 12 cm, the area of the orginal parallelogram, the question asked, is 12h. You just need to find h. After the height is increased by 3 cm. and the base length is increased by 2 cm, the new height is h+ 3 and the new base length is 14 cm so the new area is 14(h+3) and that must equal 54 cm². Solve that equation for h and then calculate 12h.

 

[M98Ranger]

Given information:
Base length of original parallelogram = 12 cm
Increase in base length = 2 cm
Increase in height = 3 cm
Increase in area = 54 cm^2

Let the original height of the parallelogram be h cm.
Using the formula for area of a parallelogram, we have:
Area = base length * height
Original area = 12 * h = 12h cm^2

After the increase in base length and height, the new area can be represented as:
New area = (12 + 2) * (h + 3) = 14 * (h + 3) cm^2

Since the increase in area is 54 cm^2, we can set up the following equation:
New area - Original area = Increase in area
14 * (h + 3) - 12h = 54
14h + 42 - 12h = 54
2h = 12
h = 6

Therefore, the original height of the parallelogram is 6 cm.
Substituting this value in the formula for area, we get:
Original area = 12 * 6 = 72 cm^2

Hence, the area of the original parallelogram is 72 cm^2.