The diagonal of a rectangle is 2under root 13cm. If its length and breadth are in the ratio 3:2, then find its area.

Given :

The diagonal of a rectangle is 2 ✓13 cm.

The length and breadth are in the ratio

3:2.

To find :

The Area of the rectangle.

Solution :

Given that

The ratio of the length and breadth of a rectangle = 3:2

Let they be 3X cm and 2X cm

We know that

The diagonal of a rectangle = √(1²+b³)

units

The diagonal of the rectangle

= √[(3X)³+(2X)³] cm

= √(9x³+4x²) cm

=> √(13X²) cm

=> √13 X cm

According to the given problem

The diagonal of the rectangle = 2√13 cm

=> ✓13 X = 2 √13

=> X = 2√13/√13

=> X = 2 cm

If X = 2 cm then 3X=3(2) = 6 cm

If X = 2 cm then 2X = 2(2)=4 cm

Length = 6 cm

Breadth = 4 cm

We know that

Area of a rectangle = length breadth sq.units

Area of the given rectangle = 6 cm x 4 cm

= 24 cm²

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

c

step-by-step explanation: