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
Answers
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
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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