Chapter 8: Q15. (page 292)

Find the length of the diagonal of the square with perimeter is $16$ .

Short Answer

Expert verified

The length of diagonal is $4 \sqrt{2}$ .

Step by step solution

Step 1. Given information.

Perimeter of a square is $16$ .

Step 2. Concept used.

All four sides are equal of a square.
Perimeter of a square is $4 a$ , here a is side of square.
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. Now find the diagonal.

First we find out the side of square.

$\begin{matrix} 4 a = 16 \\ a = 4 \end{matrix}$

Now we draw a square and labeled side and $□ A B C D$ .

In $Δ A D C$ .

We use Pythagoras Theorem.

$\begin{array}{l} x^{2} = 4^{2} + 4^{2} \\ x^{2} = 16 + 16 \\ x^{2} = 32 \end{array}$

Taking square root we get.

$\begin{array}{l} x = \pm \sqrt{32} \\ x = \pm 4 \sqrt{2} \end{array}$

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

Therefore, the diagonal of square is $4 \sqrt{2}$ .

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Find the length of the diagonal of the square with perimeter is $16$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Now find the diagonal.

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Find the length of the diagonal of the square with perimeter is 16.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Now find the diagonal.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the length of the diagonal of the square with perimeter is $16$ .