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Question -

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.



Answer -

Given:Length AB = 40 cm
Diagonal AC = 41 cm
In right triangle ABC, we have
AB2 + BC2=AC2 (By Pythagoras property)
⇒ (40)2 + BC2 =(41)2
⇒ 1600 +BC2 = 1681
⇒ BC2 = 1681 – 1600
⇒ BC2 = 81
∴ BC == 9 cm

∴ AB =DC = 40 cm and BC = AD = 9 cm (Property of rectangle)
∴ Therequired perimeter
= AB + BC + CD + DA
= (40 + 9 + 40 + 9) cm
= 98 cm

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