Question

find the lengthbof the diagonal of acsquare of side 12cm​

Answer 1

Answer:

formula for finding length of the diagonal is root over length square + breadth square

Answer 2

• The length of the diagonal of a square = 12√2 cm.

Given :

• The side of a square = 12 cm.

To Find :

• The length of the diagonal of a square.

Diagram :

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(5,1)\qbezier(1,1)(1,1)(1,5)\qbezier(1,5)(1,5)(5,5)\qbezier(5,5)(5,5)(5,1)\qbezier(5,1)(5,1)(1,5)\put(0.8,5.3){\large\sf A}\put(0.8,0.5){\large\sf B}\put(5.1,0.5){\large\sf C}\put(5.1,5.3){\large\sf D}\put(-0.3,2.7){\large\sf 12 cm}\put(5.5,2.7){\large\sf 12 cm}\put(2.5,0.5){\large\sf 12 cm}\put(2.5,5.5){\large\sf 12 cm}\end{picture}$

Solution :

Let,

A square ABCD.

AC is a diagonal.

Given,

Side of a square = 12 cm

We know that,

All sides of a square are equal.

So,

AB = BC = CD = DA = 12 cm

Diagonal AC divides a square into two triangles (∆ABC and ∆ADC).

In ∆ABC,

By the pythagoras theorem,

(Hypotenuse)² = (Perpendicular)² + (Base)²

We have,

• Hypotenuse = AC.
• Perpendicular = AB.
• Base = BC.

So,

$\implies$ AC² = AB² + BC²

The values are :

• AB = 12 cm.
• BC = 12 cm.

$\implies \tt {AC}^{2} = {(12 \: cm)}^{2} + {(12 \: cm)}^{2}$

$\implies \tt {AC}^{2} = 144 \: {cm}^{2} + 144 \: {cm}^{2}$

$\implies \tt {AC}^{2} = 288 \: {cm}^{2}$

$\implies \tt AC = \sqrt{288 \: {cm}^{2}}$

$\implies \tt AC = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \: {cm}^{2}}$

$\implies \tt AC = \sqrt{{2}^{2} \times {2}^{2} \times {3}^{2} \times 2 \: {cm}^{2} }$

$\implies \tt AC = 2 \times 2 \times 3 \sqrt{2} \: cm$

$\implies \tt AC = 4 \times 3 \sqrt{2} \: cm$

$\implies \tt AC = 12\sqrt{2} \: cm$

Hence,

The length of the diagonal of a square is 12√2 cm.