The value of a and b will be 9 / 2 and 15 / 2 respectively. The correct option is A.
What is the Pythagorean theorem?
Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The mathematical expression for the Pythagorean theorem is,
H² = P² + B²
Use the Pythagorean theorem for the whole triangle first.
( 8 + a )² = 10² + b²
64 + 16a + a² = 100 + b²
a² - b² = 100 - 64 -16a ......................................(1)
Use the Pythagorean theorem for triangle with sides a and b.
b² = 6² + a² ........................................(2)
Put the value of b² in equation 1.
a² - a² - 6² = 100 - 64 -16a
16a = 100 - 64 + 36
16a = 136 - 64
16a = 72
a = 72 / 16
a = 9 / 2
Put the value of a in equation 2.
b² = 6² + a²
b² = 36 + (81 / 4 )
b = √(225 / 4)
b = 15 / 2
Therefore, the value of a and b will be 9 / 2 and 15 / 2 respectively. The correct option is A.
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