Question

Vanakkam!
Kindly find the value of x.


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⊙ Explain every step.


Good luck :)​

Answer 1

Answer:

Vanakkam!

Step-by-step explanation:

Let AC = 52

CD = x + 13

AB = 52 - x

BD = perpendicular dropped from

point D

BC = x

In BCD

BD² = CD² - BC²

BD² = (x+13)² - x²

BD² = x² - x² + 26x + 169

BD² = 169 + 26x

value of

x = 52 - AB

using Pythagoras theorem in ACD

AC² = CD² + AD²

AD² = AC² - CD² …(1)

Now in ABD

AD² = AB² + BD² …(2)

From (1) and (2) we get

AC² - CD² = AB² + BD²

(52)² - (x+13)² = (52-x)² + 169 + 26x

2704 - x² + 26x + 169 = 2704 - 104x + x²-169 +26x

2873 - x² - x² = 2873 -104x +26x -26x

-2x² = -104x

x²/x = -104/-2

x = 52

Thus, the value of x is 52.