# ABC + BC.57. In AABC, if ZB = 90°, then find the missing quantities in the following table whichare 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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*काटकोन त्रिकोणात काटकोन करणाऱ्या बाजू a सेमी व b सेमी यांप्रमाणे आहेत ,तर सर्वांत मोठ्या बाजूची लांबी किती असेल?*

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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