Question

each side of a rhombus is 13 cm and one diagonal is 10 cm find the length of its other diagonal and the area of its rhombus

Answer 1

❄ Firstly, draw a sample diagram and note the markings.

❄ Since the diagonals of a rhombus divides it into two equal parts, so, we divide 10 cm into 5 cm and 5 cm.

❄ We apply PYTHAGORAS THEOREM and got CO = 12 cm.

❄ Diagonal measurement = (12+12)cm = 24 cm

❄ Formula for calculation of area of rhombus = (1/2)×(product of diagonals). We applied that immediately and get answer - 120 cm²

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⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

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Answer 2

Let ABCD be the Rhombus in AB = 13cm, BC=13cm, CD=13 cm, DA=13 cm, AC=10 cm.
As we know, diagonals bisect each other at right angle
so, OA= 1/2 × AC = 1/2 × 10 = 5
In right angle ∆AOB, by Pythagoras theorm.

$ab {}^{2} = oa {}^{2} + ob {}^{2}$
$13 {}^{2} = 5 {}^{2} + ob {}^{2}$
$169 = 25 + ob {}^{2}$
$ob {}^{2} = 169 - 25$
$ob ^{2} = 144$
$ob = \sqrt{144}$
Ob = 12
so, BD = 2 × OB
= 2 × 12
=24
Area of Rhombus
$\frac{1}{2} \times d1 \times d2$
$\frac{1}{2} \times ac \times bd$
$\frac{1}{2} \times 10 \times 24$
=120 cm2