Question

3. In a rectangle CALM, CA = 4 cm and AL = 3 cm. Find the
length of the diagonals CL and AM.​

Answer 1

CL = 5 cm

AM = 5 cm

Step-by-step explanation:

GIVEN

Rectangle = CALM

CA = 4 cm

AL = 3 cm

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TO FIND

The length of the diagonals CL and AM

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We know that,

Rectangle has all the angels of 90° and opposite sides of rectangle are equal

Means

CA = 4 cm

ML = 4 cm

AL = 3 cm

CM = 3 cm

___________________________

Now

Let's find the diagonals CL by Pythagoras Theorem

We know that,

( Hypotenuse )² = ( Base )² + ( Height )²

Here,

Hypotenuse = CL = ?

Base = ML = 4 cm

Height = CM = 3 cm

( Hypotenuse )² = ( Base )² + ( Height )²

( CL )² = ( ML )² + ( CM )²

( CL )² = ( 4 )² + ( 3 )²

( CL )² = 16 + 9

( CL )² = √25

CL = 5

CL = 5 cm

___________________________

Now

Let's find the diagonals AM by Pythagoras Theorem

We know that,

( Hypotenuse )² = ( Base )² + ( Height )²

Here,

Hypotenuse = AM = ?

Base = CA = 4 cm

Height = AL = 3 cm

( Hypotenuse )² = ( Base )² + ( Height )²

( CL )² = ( ML )² + ( AL )²

( AM )² = ( CA )² + ( 3 )²

( AM )² = 16 + 9

( AM )² = √25

AM = 5

AM = 5 cm