Mathematics
Assertion (A): The perimeter of the adjoining figure is (32 + x) cm.
Reason (R): x2 = 132 - 52 = 144 and x = 12 cm.
Perimeter = (32 + 12) cm
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
Mensuration
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Answer
Perimeter of the figure = sum of all the sides
= 7 + 13 + 12 + x
= (32 + x) cm
So, assertion (A) is true.
From figure,
AB = AC - BC = 12 - 7 = 5 cm
Since, ABE is a right angled triangle. Using pythagoras theorem,
⇒ AE2 = AB2 + BE2
⇒ 132 = 52 + x2
⇒ 169 = 25 + x2
⇒ x2 = 169 - 25
⇒ x2 = 144
⇒ x =
⇒ x = 12 cm
Perimeter = (32 + x) = (32 + 12) cm.
∴ Both A and R are true, and R is the correct reason for A.
Hence, option 3 is the correct option.
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