Rectangle ABCD has been subdivided into 4 regions. The areas of two of these regions are a^2 and 144. The combined area of the other two regions is 25a. What is the perimeter of the rectangle ABCD?

Question

Please help and show steps! I don't have a clue how to do this. Thank you for your time and help.

Answer 1

Are you sure the sum of the other two regions is 25a and not 24a ?
then the sum of the area would be
a^2 + 144 + 24a
= (a+12)^2

which would make it a square of sides a+12
for a perimeter of 4a + 48

Answer 2

True, but we also have

(a+9)(a+16) = a^2 + 25a + 144

Answer 3

4a+50