Question

The rectangle ABCD has AB=12cm,BC=6cm.find the length of its diagonal correct to 2 decimal places

Answer 1

Step-by-step explanation:

LENGTH OF DIAGONAL =

$\sqrt{ {lenght}^{2} + {breadth}^{2} } \\ \sqrt{ {12}^{2} + {6}^{2} } \\ \sqrt{144 + 36} \\ \sqrt{180} \\ 13.41cm$

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Answer 2

Answer:

The length of the diagonal = 13.42cm

Step-by-step explanation:

Given,

In a rectangle ABCD, AB = 12cm and BC = 6cm

To find,

The length of the diagonal

Recall the concept

All the interior angles of a rectangle = 90°

Pythagoras theorem,

In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Solution:

Since the given rectangle is ABCD, the diagonals of the rectangle are AC and BD

Since the interior angle of a rectangle = 90, we have ΔABC is  a right-angled triangle right angled at B

Hence, AC is the hypotenuse of the ΔABC.

Then by Pythagoras' theorem,

AC² = AB² + BC²

Substituting the value of AB = 12 and BC = 6 we get

AC² = 12² + 6²

= 144+36

= 180

AC = $\sqrt{180}$

=6√5

We know √5 = 2.2360

AC = 6×2.2360 = 13.416

AC = 13.42

∴ The length of the diagonal = 13.42cm

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