Question

The perimeter of square one is 36 cm greater than the perimeter of square two. The area of square one is 243 square cm more than the area of square two. Find the area of the larger square.

Answer 1

Let s= smaller square side
s+9 = larger square side because perimeter is 36 cm longer equates to each side being 4 cm longer

Now the Area of larger square is 243 sq cm larger. Remember this for later.\[A=s ^{2}\] This is the area of the small square.
\[(s+9)^{2}=s ^{2}+18s+81\] This is the area of large square

Answer 2

Remember their difference is 243 cm sq.
\[s ^{2}+18s+81 - s ^{2}=243 cm sq\]

\[18s=162\]
s=9
s+9=18

There you have it small square has sides of 9 cm the larger sq is 18 cm

Answer 3

Verification, Perimeter of small sq is 36 cm, large sq is 72 36 larger!
Area is small sq is 81 sq cm, area of large sq is 324 sq cm diff of 243

Seems to check out