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fieryanswererft

Answer:

20 cm is the side of the bigger square.

Step-by-step explanation:

Let one square's side be x,

Then another squares side will be ( x + 5 )

  • Formula for square's area: side²

Total area:

  • x² + ( x + 5 )² = 625
  • x² + x² + 10x + 25 = 625
  • 2x² + 10 x + 25 - 625 = 0
  • 2x² + 10x - 600 = 0
  • 2(x² + 5x - 300) = 0
  • x² + 5x - 300 = 0
  • x² + 20x - 15x - 300 = 0
  • x(x + 20) -15(x + 20) =0
  • x = -20, 15
  • x = 15

So one square's side is 15 cm

Then the bigger square has:

  • x + 5
  • 15 + 5
  • 20 cm
Xignerso

Let the length of each side of the smaller square be [tex]x[/tex]. Then area of the square is [tex]x^2[/tex].

The length of each side of the larger square will be [tex]x+5[/tex].

Then the area of the square will be [tex](x+5)^2[/tex]

As per the question the area of the larger square is four times the square of the smaller square.

Therefore [tex](x+5)^2 = 4x x^2[/tex]

[tex]→ x^2 +10x +25 = 4x^2[/tex]

[tex]→ 3x^2 -10x -25 = 0[/tex]

[tex]→ 3x^2 +5x-15x - 25 = 0[/tex]

[tex]→ (3x + 5)(x-5) = 0[/tex]

We get [tex]x=5[/tex], and [tex]x=-\frac{5}{3}[/tex]

Considering the positive value we get [tex]x+5=5+5=10[/tex]

Therefore the side of the squares are [tex]5[/tex] cms and [tex]10[/tex]cm.

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