Identify the perimeter and area of a square with diagonal length 11in. give your answer in simplest radical form.

Perimeter = 22*sqrt(2)Area = 60.5 inchesD

Step-by-step explanation:

Remark

You need 2 facts.

A square has 4 equal sides. 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^22a^2 = c^2

Givens

c = 11

Solution

2a^2 = 11^22a^2 = 121                    Divide by 2a^2 = 121/2                  Take the square root of both sidessqrt(a^2) = sqr(121/2)    a = 11/sqrt(2)                Rationalize the denominatora = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]a = 11 * sqrt(2) / 2

Perimeter

P = 4s

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

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

Area

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