Maximizing Parallelogram Area: A Mathematical Approach

[travishillier]

Need some serious math help ...

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 ...

 

[Inspector Gadget]

area of a parallelogram = b*h

area of "old" p-gram = b*h = 12h cm
area of "new" p-gram = (b+2 cm)(h+3 cm) = (12 cm + 2 cm)(h+3 cm) = (14 cm)(h+3 cm) = 14h cm + 42 cm^2

So, the area increased by 54 cm^2, so:

(area "new" p-gram) - (area "old" p-gram) = 54cm^2

14h cm + 42 cm^2 - 12h cm = 54cm^2
2h cm + 42 cm^2 = 54cm^2
2h cm = 12 cm^2
h = 6 cm

So, the original height is 6 cm.

Original formula: A=b*h=(12 cm)(6 cm) = 72 cm^2

And, just to check with the new area...

A=(b+2)(h+3)=(12 cm +2 cm)(6 cm + 3 cm)=(14 cm)(9 cm) = 126 cm^2

And make sure the difference is 54: 126 cm^2 - 72 cm^2 = 54cm^2

 

[travishillier]

hey, thanks a lot for the info on this question .. you could not of helped me any more ... thanks a mill