Answer of b with full working plz

b = 21.9 cm

Step-by-step explanation:

Please see attached photo for details.

We'll begin by calculating the length of BC. This can be obtained by using pythagoras theory as illustrated below:

AB = 41 cm

AC = 9 cm

BC =?

AB² = BC² + AC²

41² = BC² + 9²

1681 = BC² + 81

Collect like terms

1681 – 81 = BC²

1600 = BC²

Take the square root of both side

BC = √1600

BC = 40 cm

Next, we shall determine CD.

BC = BD + CD

BD = CD

BC = CD + CD

BC = 2CD

BC = 40 cm

40 = 2CD

Divide both side by 2

CD = 40/2

CD = 20 cm

Finally, we shall determine the value of 'b' this can be obtained as follow:

AC = 9 cm

CD = 20 cm

AD = b cm

AD² = CD² + AC²

b² = 20² + 9²

b² = 400 + 81

b² = 481

Take the square root of both side

b = √481

b = 21.9 cm.

step-by-step explanation: