Respuesta :
The value of a is 184. The above solution is derived using Pythagoras' theorem .
by using Pythagoras' theorem we will get 3 equations
- [tex]x^2 + 7^2 = r^2[/tex]
- [tex](3-x)^2 + (\frac{\sqrt{a}}{2}) ^2 = r^2[/tex]
- [tex]5^2 + (3+ (3- x))^2 = r^2[/tex]
now equating 1 and 3 equations we will get,
[tex]x^2 + 7^2 = 5^2 + (3+ (3- x))^2[/tex]
[tex]x^2 + 7^2 = 5^2 + (6^2+ x^2 + 12x)[/tex]
after solving this equation we get x = 1
now putting the value of x in equation 1 we get
[tex]r^2 = x^2 + 7^2\\r^2 = 1 + 49\\r^2 = 50[/tex]
now putting the value of r in equation 2 we get
[tex](3-x)^2 + (\frac{\sqrt{a}}{2}) ^2 = r^2[/tex]
[tex](3-1)^2 + (\frac{\sqrt{a}}{2}) ^2 = 50[/tex]
on solving the equation, we get
a = 184
What is Pythagoras' theorem?
- The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry.
- According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.
To learn more about Pythagoras' theorem with the given link
https://brainly.com/question/343682
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