Answer:
The small square has a 6cm side; the larger square has a 8cm side.
Step-by-step 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:
[tex]x^{2} + (x +2)^{2} = 100[/tex] Expand then recombine
[tex]x^{2} +x^{2} +4x +4 = 100[/tex]
[tex]2x^{2} + 4x +4 = 100[/tex] becomes [tex]2x^{2} + 4x = 96[/tex] divide by 2 to simplify and then=0
[tex]x^{2} +2x -48 = 0[/tex] 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 ! ! [tex]6^{2} = 36[/tex]
now 6+2 for square 2: [tex]8^{2} = 64[/tex]
36 + 64 = 100 TRUE!
