Triangle ABC is right angled at B. BD is an altitude…

In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
John was an artist (1)______ profession. He was very (2)______ at his work and could
(3)______ any subject he could think of, but circumstances forced him to (4)______ in
(5)______ the work of renowned artists.

Triangle ABC is right angled at B. BD is an altitude intersecting AC at D. If AC = 9 and CD = 3 cm, then find the measures of AB (in cm).

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 3√6

Let the length of BD be x.

AD = AC - CD = 9 - 3 = 6 cm

Applying Pythagoras theorem in ∆ABD -

AB² = AD² + BD²

AB² = x² + 36 ...(1

Applying Pythagoras theorem in ∆BCD -

BC² = BD² + CD²

BC² = x² + 9 ....(2

Applying Pythagoras theorem in ∆ABC -

AC² = AB² + BC²

9² = x² + 36 + x² + 9

2x² = 36

x² = 18

x = √18 = 3√2 cm

From eq(1 -

AB² = x² + 36

AB² = (3√2)² + 36 = 18 + 36 = 54

AB = 3√6 cm

SSC CGL 2021 PYQ — Question 58