Question

If the diagonals of a rhombus are of measure 10cm and 24cm. Find the sides of rhombus.​

Answer 1

★ How to do :-

Here, we are given with a diagram of a rhombus which has two diagonals. One of them measures 10 cm and the other diagonal measures 24 cm. As a result the interior of the rhombus can form four right angles. We know that when there are two diagonals in a figure they should be cut in two equal parts. So, here the concepts used is the pythagoras theorem, in which it is applied only for a right-angled triangle. So, let's solve!!

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➤ Solution :-

Let's find the measurement of the side AD by using the pythagoras theorem. We know that a diagonal divides into two equal parts. So,

${\tt \leadsto {OA}^{2} + {OD}^{2} = {AD}^{2}}$

Let's substitute the values.

${\tt \leadsto {12}^{2} + {5}^{2} = {AD}^{2}}$

Find the square numbers of 12 and 5.

${\tt \leadsto 144 + 25 = {AD}^{2}}$

Add the square numbers of 12 and 5.

${\tt \leadsto 169 = {AD}^{2}}$

Now, find the value of AD.

${\tt \leadsto AD = \sqrt{169}}$

${\tt \leadsto AD = 13 \: \: cm}$

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We know that all the sides of a rhombus measures equal to each other i.e, all the sides are equal.

So, here we can say that

$\to \tt \orange{\boxed{\sf AB = 13 \: \: cm}}$

$\to \tt \orange{\boxed{\sf BC = 13 \: \: cm}}$

$\to \tt \orange{\boxed{\sf CD = 13 \: \: cm}}$

$\to \tt \orange{\boxed{\sf DA = 13 \: \: cm}}$