Question

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

Answer 1

the length of its another diagonal is 10 cm

Answer 2

Answer:

The other diagonal of Rhombus is 12 cm.

Area of the Rhombus is 120 centimeter square.

Step-by-step explanation:

Given : Each side of rhombus is 13 cm and one diagonal is 10 cm.

To find : The length of its other diagonal and the area of the Rhombus?

Solution :

One side rhombus = 13 cm

Length of one diagonal = 10 cm

Property of rhombus,

Diagonals of rhombus bisect each other at 90 degree.

Now, Taking 1/4 portion of rhombus i.e, triangle.

Base = 5 cm (half of diagonal)

Hypotenuse = 13 cm

Applying Pythagoras theorem,

${h}^{2}={b}^{2}+{p}^{2}$

${13}^{2}={5}^{2}+{p}^{2}$

$169=25+{p}^{2}$

${p}^{2}=169-25$

$p=\sqrt{144}$

$p=12$

So, The other diagonal of Rhombus is 12 cm.

Area of rhombus is

$A=\frac{1}{2}\times (\text{product of diagonal})$

$A=\frac{1}{2}\times (24\times 10)$

$A=120cm^2$

Therefore, Area of the Rhombus is 120 centimeter square.