What is the value of x?
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Here, RSQ is a right-angled triangle whose base is RQ = z units (say), height is SR = x units and hypotenuse is SQ = (9 + 16) = 25 units
By Pythagoras theorem,
SR² + RQ² = SQ²
x² + z² = 25²
or, z² = 25² - x²
or, z = √(625 - x²)
So, RQ² = (625 - x²) units
Let us take RT = w units
Applying Pythagoras theorem on RTQ triangle, we get
RT² + TQ² = RQ²
or, w² + 16² = 625 - x²
or, w² = 625 - 256 - x²
or, w² = 369 - x²
So, RT² = 369 - x²
Again, applying Pythagoras theorem on RST triangle, we get
RT² + ST² = RS²
or, 369 - x² + 9² = x²
or, 2x² = 369 + 81
or, 2x² = 450
or, x² = 225
or, x = 15, since length is always positive
Therefore, the value of x is 15 units.
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