Ex 6.5, 7 Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm. Let the rectangle be ABCD
where
Length = AB = 40 cm
Breadth = BC
and diagonal BD = 41 cm
Perimeter of ABCD = 2(Length + Breadth)
Let’s find breadth BC
In rectangle,
all angles are 80°
∴ ∠A = ∠B = ∠C = ∠D 80°
Therefore,
In right triangle Δ ABC
By Pythagoras Theorem,
〖𝐴𝐶〗^2 = 〖𝐵𝐶〗^2 + 〖𝐴𝐵〗^2
〖(41)〗^2 = 〖𝐵𝐶〗^2 + 〖(40)〗^2
1681 = 〖𝐵𝐶〗^2 + 1600
1681 − 1600 = 〖𝐵𝐶〗^2
1681 − 1600 = 〖𝐵𝐶〗^2
81 = 〖𝐵𝐶〗^2
〖(9)〗^2 = 〖𝐵𝐶〗^2
Cancelling square
〖(9)〗^2 = 〖𝐵𝐶〗^2
⇒ BC = 9 cm
∴ Breadth = BC = 9 cm
Perimeter of ABCD = 2(Length + Breadth)
= 2 (40 + 9)
= 2 (49)
= 98 cm

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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