Question

Need help on geometry right answers only I’m giving 25 points

Answer 1

What is the perimeter of a square with a diagonal measuring 5 feet?
14.142 feet
12.5 feet
20 feet
25 feet

In answering this problem,
First, consider the properties of the given figure. Since the given figure is a square and we know that a square has equal sides and has an angle of 90degrees each side.
Consider solving this problem with this formula:
Diagonal= sqrt(2) * side
Substitute: diagonal=5
5/sqrt(2)= side
side=3.54=a

Perimeter of a square is:
P=a+a+a+a
P=4(a)
P= 4(3.54)
P= 14.142 feet

Answer 2

Answer: first choice 14.142 ft

Step-by-step explanation:


1) Side length of the square: x


2) Use the Pythagorean theorem to relate the side lenght with the diagonal:

diagonal² = x² + x² = 2x²

3) Clear x:

x² = diagonal² / 2

⇒x = √(diagonal² / 2) = diagonal /√2 = diagonal √2 / 2

4) subsitute diagonal = 5 ft

⇒ x = 5 ft √2 / 2 ≈ 3.536 ft

5) The perimeter of the square is 4 times the side length:

Perimeter = 4 × 3.536 ft = 14.142 ft