Question

The side of one square is 2 cm longer than the side of the second square. If the sum of the areas is 100 cm², find the length of the side of each square.

Answer 1

The small square has a 6cm side; the larger square has a 8cm side.

Explanation:

Set up an equation that uses the given facts and common knowledge:

The area of a square is the length of the side times itself, that is "squared"!

You have 2 different squares; their total area is 100.

Use x to be the side of Square 1, and x+2 for the square that has 2cm longer sides. Here's the equation:

`x^(2) + (x +2)^(2) = 100` Expand then recombine

`x^(2) +x^(2) +4x +4 = 100`

`2x^(2) + 4x +4 = 100` becomes
`2x^(2) + 4x = 96` divide by 2 to simplify and then=0

`x^(2) +2x -48 = 0` Now factor that.

(x+8)(x-6) = 0 Set each factor to equal zero and solve for x.

x + 8 = 0 x - 6 = 0

x= -8 x= 6 Squares don't have negative sides, so use the +6.

Back to square 1 ! !
`6^(2) = 36`

now 6+2 for square 2:
`8^(2) = 64`

36 + 64 = 100 TRUE!