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gavmur [86]
3 years ago
11

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

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

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

<em><u>Perimeter</u></em>

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

<em><u>Area</u></em>

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


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\begin{array}{rcl}23 944.00 & = & 1.025 P\\P & = & \dfrac{23 944.00 }{1.025} \\\\& = & \mathbf{23 360.00} \\\end{array}\\\text{Carol originally invested $\large \boxed{\textbf{\pounds23 360.00}}$ in her account.}

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1 Jan 2014      P = £23 360.00

1 Jan 2015     A =    23 944.00

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                     P =     22 944.00

1 Jan 2016    A =    £23 517.60

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