Question

The area of a square deck is w²+10w+25. What is the side length of the deck. If w=4, what is the area and what is the perimeter.

Answer 1

Each Side of the squared deck = (w + 5)

If w = 4, the area of the square = 81 sq units

perimeter of the square = 36 units,

Explanation:

The area of the square deck is
`w^(2)   + 10w  + 25`

Now, Area of the Square is
`(Side)^(2)`

Factorizing the given expression, we get

`w^(2)   + 10w  + 25 = w^(2)   + 5w  + 5w + 25`

or,
`w(w+5) +5(w+5) = 0`

or,
`(w+5)(w+5) =0`

⇒
`(w+5)^(2)  = 0`

⇒ The area of the Square deck is
`(w+5)^(2)`

Comparing it with the formula for area,

we get each Side of the squared deck = (w + 5)

Now, if w = 4, then each side = 4+ 5 = 9 units

Hence, the area of the square = 9 x 9 = 81 sq units

Perimeter of the squire = 4 x SIDE = 4 x 9 = 36 units

Answer 2

For the given square area expression, the Area of Square is 81 unit² And the perimeter of square is 36 units

Explanation:

Given as :

The area of a square deck is w² + 10 w +25

The value of w = 4

Let the side length of deck = S

Now put the value to w in given square area

I.e w² + 10 w +25

Or, (4)² + (10 × 4) + 25

Or, 16 + 40 + 25

So, Area of square with side s = 81 unit²

∴ Area of square = side × side

Or, 81 unit² = s²

∴ s =
`√(81)` = 9 unit

So , Side = 9 unit

Now perimeter of square = 4 × side

I.e perimeter of square = 4 × 9

Or, perimeter of square = 36 unit

Hence for the given square area expression, the Area of Square is 81 unit² And the perimeter of square is 36 units Answer