ABC + BC.
57. In AABC, if ZB = 90°, then find the missing quantities in the following table which
are marked by question

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​

2 thoughts on “ABC + BC.<br />57. In AABC, if ZB = 90°, then find the missing quantities in the following table which<br />are marked by question”

  1. Given :- ABC, if ∠B = 90°, then find the missing quantities in the following table :-

    AB BC AC

    (1) 12 ? 37

    (2) 21 20 ?

    (3) 39 ? 89

    (4) ? 55 73

    Solution :-

    we know that,

    • Angle opposite to right angle = Hypotenuse = AC
    • AB² + BC² = AC² (Pythagoras theorem) .

    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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  2. 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

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