Respuesta :
Answer:
For the given square area expression, the Area of Square is 81 unit² And the perimeter of square is 36 units
Step-by-step 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 = [tex]\sqrt{81}[/tex] = 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
Answer:
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,
Step-by-step explanation:
The area of the square deck is [tex]w^{2} + 10w + 25[/tex]
Now, Area of the Square is [tex](Side)^{2}[/tex]
Factorizing the given expression, we get
[tex]w^{2} + 10w + 25 = w^{2} + 5w + 5w + 25[/tex]
or, [tex]w(w+5) +5(w+5) = 0[/tex]
or, [tex](w+5)(w+5) =0[/tex]
⇒[tex](w+5)^{2} = 0[/tex]
⇒ The area of the Square deck is [tex](w+5)^{2}[/tex]
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
