Question

Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!

Answer 1

Answer:

• Perimeter = 22*sqrt(2)
• Area = 60.5 inches
• D

Step-by-step explanation:

Remark

You need 2 facts.

1. A square has 4 equal sides.
2. It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

• a^2 + a^2 = c^2
• 2a^2 = c^2

Givens

• c = 11

Solution

• 2a^2 = 11^2
• 2a^2 = 121                    Divide by 2
• a^2 = 121/2                  Take the square root of both sides
• sqrt(a^2) = sqr(121/2)    
• a = 11/sqrt(2)                Rationalize the denominator
• a = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]
• a = 11 * sqrt(2) / 2

Perimeter

P = 4s

• P = 4*11*sqrt(2)/2
• P = 44*sqrt(2)/2
• P = 22*sqrt(2)

You don't need the area. The answer is D

Area

• Area = s^2
• Area = (11*sqrt(2)/2 ) ^2
• Area = 121 * 2 / 4
• Area = 60.5