ABC + BC.

57. In AABC, if ZB = 90°, then find the missing quantities in the following table which

are marked by question sign (?):

Sr. No.

AB

BC

AC

(1)

12 cm

(?)

37 cm

nsh

(2)

21 cm

20 cm

(?)

(3)

39 cm

89 cm

(?)

55 cm

od

(4)

(?)

73 cm

# ABC + BC.

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:- ABC, if ∠B = 90°, then find the missing quantities in the following table :-GivenAB BC AC

(1) 12 ? 37

(2) 21 20 ?

(3) 39 ? 89

(4) ? 55 73

:-Solutionwe know that,

so,

→ AB² + BC² = AC²

→ 12² + BC² = 37²

→ BC² = 37² – 12²

→ BC² = (37 + 12)(37 – 12)

→ BC² = 49 * 25

→ BC² = 7² * 5²

→ BC² = (7 * 5)²

→ BC = 35 (Ans.1)

similarly,

→ AB² + BC² = AC²

→ 21² + 20² = AC²

→ AC² = 441 + 400

→ AC² = 841

→ AC = √(841)

→ AC = 29 (Ans.2)

and,

→ AB² + BC² = AC²

→ 39² + BC² = 89²

→ BC² = 89² – 39²

→ BC² = (89 + 39)(89 – 39)

→ BC² = 128 * 50

→ BC² = 6400

→ BC = √(6400)

→ BC = 80 (Ans.3)

also,

→ AB² + BC² = AC²

→ AB² + 55² = 73²

→ AB² = 73² – 55²

→ AB² = (73 + 55)(73 – 55)

→ AB² = 128 * 18

→ AB² = 2304

→ AB² = √(2304)

→ AB = 48 (Ans.4)

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Step-by-step explanation:ABC + BC.

57. In AABC, if ZB = 90°, then find the missing quantities in the following table which

are marked by question sign (?):

Sr. No.

AB

BC

AC

(1)

12 cm

(?)

37 cm

nsh

(2)

21 cm

20 cm

(?)

(3)

39 cm

89 cm

(?)

55 cm

od

(4)

(?)

73 cm