Question

The diagonals of a rhombus are 8 cm and 15 cm. Find its side.

Answer 1

let ABCD be a rhombus
diagonals :-
AC= 8cm
DB=15 cm
let AC and DB meet at a point O
AD² = AO² + OD²
AD² = 4² + 7.5²
AD² = 16 + 56.25
AD² = 72.25
AD = √72.56
AD = 8.5
HENCE, EACH SIDE OF THE RHOMBUS IS 8.5 CM....

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Answer 2

The side of the rhombus is, 8.5 cm

Given : The diagonals of a rhombus are 8 cm and 15 cm.

To find : The side of the rhombus.

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

Now, we know that :

$a = \frac{ \sqrt{ {p ^{2} } + {q}^{2} } }{2}$

Here,

• a = side of the rhombus
• p = first diagonal of the rhombus
• q = second diagonal of the rhombus

In this case,

• a = ? (unknown quantity)
• p = 8cm
• q = 15cm

By, putting the available data in the above mentioned, mathematical formula, we get :

$a = \frac{ \sqrt{ {8}^{2} + {15}^{2} } }{2}$

$a = \frac{ \sqrt{64 + 225} }{2}$

$a = \frac{ \sqrt{289} }{2}$

$a = \frac{17}{2}$

$a = 8.5$

So, the side of the rhombus = a cm = 8.5 cm

Hence, the side of the rhombus is 8.5 cm