1.5 Applications and Modeling with Quadrant

Question

The length of each side of a square is 3 in. More than the length of each side of a smaller square. The sum of the areas of the squares in 65 in squared. Find the lengths of the sides of two squares

Answer 1

The smaller square has side measure N.

So it's area is n^2

the bigger square has side measure (n+3).

So it's area is (n+3)^2

(n+3)^2 + n^2 = 65

n^2 + 6n + 9 + n^2 = 65

2n^2 + 6n + 9 = 65

2n^2 + 6n - 56 = 0

n^2 + 3n - 28 = 0

( n + 7 )( n - 4 ) = 0

n+7=0 results in negative measures

n-4 = 0 ---> n = 4

Smaller square has side measure 4 and area 16.

Larger square has side measure 7 and area 49.

Note that the total area is 65