Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm. Complete the following activity.

Activity: As shown in figure LMNT is a reactangle.

∴ Area of rectangle = length × breadth

∴ Area of rectangle = `square` × breadth

∴ 192 = `square` × breadth

∴ Breadth = 12 cm

Also,

∠TLM = 90° ......[Each angle of reactangle is right angle]

In ∆TLM,

By Pythagoras theorem

∴ TM^{2} = TL^{2} + `square`

∴ TM^{2} = 12^{2} + `square`

∴ TM^{2} = 144 + `square`

∴ TM^{2} = 400

∴ TM = 20

#### Solution

As shown in figure LMNT is reactangle.

∴ Area of rectangle = length × breadth

∴ Area of rectangle = **16** × breadth

∴ 192 = **16** × breadth

∴ Breadth = `192/16`

∴ Breadth = 12 cm

i.e., TL = 12 cm and LM = 16 cm ......(i)

Also, ∠TLM = 90° ......[Each angle of reactangle is right angle]

In ∆TLM, By Pythagoras theorem

∴ TM^{2} = TL^{2} + **LM ^{2}**

∴ TM^{2} = 12^{2} + **16 ^{2} **......[From (i)]

∴ TM^{2} = 144 + **256**

∴ TM^{2} = 400

∴ TM = 20