SOLUTION: Two squares have a combined area of 17cm2. The sum of the perimeter of the squares is 20cm. Find the lengths of the squares.

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Question 694467: Two squares have a combined area of 17cm2. The sum of the perimeter of the squares is 20cm. Find the lengths of the squares.
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Length of first square = A
Length of second square = B
"Two squares have a combined area of 17cm2"
so +A%5E2+%2B+B%5E2+=+17+ ..... Eq(1)
"The sum of the perimeter of the squares is 20cm"
so +4A+%2B+4B+=+20+
+A+%2B+B+=+5+
+A+=+5-B+ ..... Eq(2)
Substituting Eq(2) into Eq(1) gives:
+%285-B%29%5E2+%2B+B%5E2=17+
+25-10B%2BB%5E2+%2B+B%5E2=17+
+2B%5E2-10B%2B8=0+
+B%5E2-5B%2B4=0+
+%28B-1%29%28B-4%29=0+
so B=1 or B=4
Subs B=1 into Eq(2) gives: A=5-1=4
Subs B=4 into Eq(2) gives: A=4-1=1
These are complementary solutions so one square has side 1, the other has side 4
Check:
Square with side 1, Area=1, Perimeter=4
Square with side 4, Area=16, Perimeter=16
Sum of Areas=17, sum of perimeters=20