Question

The side of a square is 5 cm more than the side of another square. If the sum of their areas is 625 cm², then the side of the bigger square is​

Answer 1

Let the length of each side of the smaller square be
`x`. Then area of the square is
`x^2`.

The length of each side of the larger square will be
`x+5`.

Then the area of the square will be
`(x+5)^2`

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

Therefore
`(x+5)^2 = 4x x^2`

`→ x^2 +10x +25 = 4x^2`

`→ 3x^2 -10x -25 = 0`

`→ 3x^2 +5x-15x - 25 = 0`

`→ (3x + 5)(x-5) = 0`

We get
`x=5`, and
`x=-(5)/(3)`

Considering the positive value we get
`x+5=5+5=10`

Therefore the side of the squares are
`5` cms and
`10`cm.

Answer 2

20 cm is the side of the bigger square.

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