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 $6 \sqrt{2}$ .

Step by step solution

Step 1. Given information.

The square has a diagonal of length $12$ .

Step 2. Concept used.

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

Step 3. Calculation.

First we draw a square with diagonal $12$ and labeled $□ A B C D$ .

Let side be x.

In $Δ A D C$ .

$∠ A D C = 90^{°} and \vec{A D} = \vec{D C} = x$

Therefore, $Δ A D C$ is a right angle triangle.

We use Pythagoras Theorem.

$\begin{matrix} x^{2} + x^{2} = 12^{2} \\ 2 x^{2} = 144 \\ x^{2} = 72 \end{matrix}$

Taking square root we get.

$\begin{array}{l} x = \pm \sqrt{72} \\ x = \pm 6 \sqrt{2} \end{array}$

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

Therefore, the length of side is $6 \sqrt{2}$ .

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Calculation.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Statistics

Geometry

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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