1. Each side of a rhombus is 13 cm and one diagonal is 10 cm. Find (1) the length of its other diagonal (ii) the area of the rhombus. pls tell me correct answer with every formula and steps because my tution teacher isn't telling me :( maine kafi baar kiya magar unhe sahi lga hi nhi rha :(
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Class 8
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Each sides of a rhombus is 13cm and one diagonal is 10cm. Find
(i) the length of its other diagonal
(ii) the area of the rhombus
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Solution
verified
Verified by Toppr
(i) Given
Side of rhombus =13 cm
Length of diagonal AC=10 cm
∴ OC=5 cm
Since, the diagonals of a rhombus bisect each other at right angles.
So, △BOC is right-angled.
Then, by Pythagoras Theorem we have
BC 2=OC 2 +OB 2
⇒13 2 =52+OB 2
⇒OB 2 =169−25=144
⇒OB= 144 =12cm
Hence,
diagonal BD=2×OB=2×12=24 cm
(ii) Area of rhombus = 21 ×d 1 ×d 2= 21×10×24=12 cm 2
(i) Given
Side of rhombus =13 cm
Length of diagonal AC=10 cm
∴ OC=5 cm
Since, the diagonals of a rhombus bisect each other at right angles.
So, △BOC is right-angled.
Then, by Pythagoras Theorem we have
BC ^2 = OC ^2 + OB ^2
⇒13^2 = 5 ^2+OB^2
⇒OB ^2 =169−25=144
⇒OB^2= 144
=12cm
Hence,
diagonal BD=2×OB=2×12=24 cm
(ii) Area of rhombus = 1 upon 2×d1×d2
1 upon 2 ×10×24=12cm^2