Question

The length of a diagonals of a rombhus are 16cm 12cm find the length of its sides

Answer 1

Answer:

10 cm

Step-by-step explanation:

As per the provided information in the given question, we have:

• Length of diagonals of a rhombus are 16 cm and 12 cm.

We've been asked to calculate the length of side of rhombus.

Let us suppose ABCD as the rhombus with AC and BD as it's diagonals. We know, diagonals of rhombus bisects each other perpendicularly. In order to calculate the length of side of rhombus, we firstly take ∆AOB. So,

• Length of AO = 8 cm (½ of the length of AC.)
• Length of BO = 6 cm (½ of the length of BD.)
• Angle AOB = 90°

By using pythagoras theorem we can find the length of other side of triangle ABC i.e., length of AB.

$\odot$ When a triangle is right angled, then the square of it's hypotenuse equals to the sum of square of opposite side and square of it's base is called Pythagoras theorem.

$\twoheadrightarrow\quad\sf{{AB}^{2}={AO}^{2}+{BO}^{2}}$

Substitute value of AO and BO in order to perform addition.

$\twoheadrightarrow\quad\sf{{AB}^{2}={8}^{2}+{6}^{2}}$

Writing the squares of the numbers.

$\twoheadrightarrow\quad\sf{{AB}^{2}=64+36}$

Performing addition.

$\twoheadrightarrow\quad\sf{{AB}^{2}=100}$

Transposing the square from LHS to RHS.

$\twoheadrightarrow\quad\sf{AB=\sqrt{100}}$

Writing the root of the number.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{AB=\frak{10\: cm}}}}$

❝ Therefore, the length of side of the rhombus is 10 cm. ❞