Question

each side of a rhombus is 13 cm and one diagonal is 10 cm find the length of the Other diagonal

Answer 1

The diagonals of rhombus bisect each other at right angle.

Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 10 cm , OA =1/2×AC=
OA= (½) × 10= 5 cm
OA= 5 cm


AB = 13 cm (given)

In ∆ AOB
By Pythagorean theorem
AB²= 0B²+ OA²
13² = OB² + 5²
169 = OB² + 25

OB²= 169 – 25
OB² =144
OB= √144

OB= 12 cm
Diagonal BD = 2 x 12= 24 cm

Hence, the length of other Diagonal = 24 cm

HOPE THIS WILL HELP YOU....

Answer 2

$\huge \pink{Answer} \\ \\ \huge \pink{24cm}...$

Solution

Let ABCD is a Rhombus where E is a point there both diagonals intersect each other.

Given

Lengths AD = 13cm

$Diagonals = 10cm \\ \\ BD = 2MD \\ \\ MD = \frac{1}{2} \times 10 \\ \\MD = 5$
From property of Rhombus.

Diagonal of Rhombus bisect each other at 90° angles.

In ∆ AMD

Using Pythagoras theorem.

$AD^2 = AM^2 + MD^2 \\ \\ 13^2 = Am^2 + 5^2 \\ \\ Am^2 = 13^2 - 5^2 \\ \\ Am^2 = 169 - 25 \\ \\ Am^2 = \sqrt{144} \\ \\ = \sqrt{12 \times 12} \\ \\ Am = 12cm$
BD = 2Am

BD = 2 × 12cm

BD = 24 cm.

Therefore the lengths of diagonals of Rhombus are 24cm

Be brainly