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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
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
∴ TM2 = TL2 + LM2
∴ TM2 = 122 + 162 ......[From (i)]
∴ TM2 = 144 + 256
∴ TM2 = 400
∴ TM = 20
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