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Chapter 8: Q16. (page 292)

Find the length of the side of a square with diagonal of length 12.

Short Answer

Expert verified

The length of side is 62.

Step by step solution

01

Step 1. Given information.

The square has a diagonal of length 12.

02

Step 2. Concept used.

  1. A square has all four sides are equal and each interior angle is right angle.
  2. Pythagoras Theorem state that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.
03

Step 3. Calculation.

First we draw a square with diagonal 12and labeled 鈻�ABCD.

Let side be x.

In 螖ADC.

鈭�ADC=90掳andAD鈫�=DC鈫�=x

Therefore,螖ADC is a right angle triangle.

We use Pythagoras Theorem.

x2+x2=1222x2=144x2=72

Taking square root we get.

x=卤72x=卤62

Since, distance is always a positive quantity. So, we neglect negative sign.

Therefore, the length of side is 62.

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