Question

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

∴ TM² = TL² + `square`

∴ TM² = 12² + `square`

∴ TM² = 144 + `square`

∴ TM² = 400

∴ TM = 20

Answer 1

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

∴ TM² = TL² + LM²

∴ TM² = 12² + 16²     ......[From (i)]

∴ TM² = 144 + 256

∴ TM² = 400

∴ TM = 20