Question

Each side of a rhombus is
$3 \sqrt{5} m$
and its one diagonal is twice the other, then find the area of the quadrilateral​

Answer 1

Answer:

Step-by-step explanation:

Answer:

Area of rhombus = 36 cm²

Step-by-step explanation:

Given :

Each side of rhombus is 3√5 cm.

Let the length of one diagonal be x

Length of other diagonal = 2x

As We know:

Diagonals of a rhombus bisect each other at 90°.

Let's Suppose:

ABCD is a rhombus and AC and BD are the two diagonals of the rhombus which bisect each other at 90°.

By applying Pythagoras theorem,

AB² = AO² + BO²

(3√5)² = (2x/2)² + (x/2)²

45 = x² + x²/4

45 = (4x² + x²)/4

45 × 4 = 5x²

x² = 180/5

x = √36 = 6

Length of one diagonal = x = 6 cm

Length of other diagonal = 2x = 2 × 6 = 12 cm

Area of Rhombus = ½(product of its diagonals) sq. units

Hence,  

Area of rhombus = 36 cm².

Hope it helps you.