RRB NTPC 28 April 2016 Paper

Question : 54 of 100

Marks: +1, -0

In a right-angled triangle, the longest side is 1 cm longer than the middle side and the middle side is 49 cm longer than the shortest side. Calculate the length of the shortest side.

11 cm
10 cm
21 cm
60cm

Validate

Solution:

(1) Given in a right angle Δ
H = B + 1
B = 49 + P
We know that in a right angled triangle,

{ P } ^ { 2 } + { B } ^ { 2 } = { H } ^ { 2 }

(From Pythagoras theorem)

\⇒ ( B - 49 ) ^ { 2 } + B ^ { 2 } = ( B + 1 ) ^ { 2 }

\⇒ B ^ { 2 } + ( 49 ) ^ { 2 } - 98 B + B ^ { 2 } = B ^ { 2 } + 1 + 2 B

\⇒ B ^ { 2 } - 10 0 B + 2400 = 0

B = { 100± √ { 10000 - 9600 } } /{ 2 }

\⇒ B = { 100 ± √ { 400 } }/ { 2 } = 60,40

B > 49; B ≠ 40 and B=60
P = B − 49 = 60 − 49=11 cm

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