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

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:  

$x^{2} + (x +2)^{2} = 100$   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!