In figure s and t trisect the side qr
Asked by admin @ in Math viewed by 293 People
a triangle PQR is right angeled at Q and points S and T trisect side QR.prove that 8PT^2= 3PR^2+5PS^2.
Answered by admin @
Let,QS=x
QS=ST=TR=x
QT=2x
QR=3x
In ΔPQT, ∠Q=90°
PT²=PQ²+QT²
=PQ²+4x² -------------- 1
In ΔPQR, ∠Q=90°
PR²=PQ²+QR²
=PQ²+9x²
In ΔPQS, ∠Q=90°
PS²=PQ²+QS²
=PQ²+x²
From eq.1
8PT²=8PQ²+32x²--------------------- eq.2
[by multiplying eq.1 by 8]
3PR²+5PS²=3(PQ²+9x²)+5(PQ²+x²)
=3PQ²+27x²+5PQ²+5x²
=8PQ²+32x²
=8(PQ²+4x²)
=8PT² [from eq.2]
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