Question

In triangle pqr S is the midpoint of qr and pt is perpendicular to qr prove that pr 2 is equal to ps 2+qr ×
st +qr upon 2 the whole square

Answer 1

Answer:

QED

Step-by-step explanation:

In triangle pqr S is the midpoint of qr and pt is perpendicular to qr prove that pr 2 is equal to ps 2+qr ×  st +qr upon 2 the whole square

to Prove pr² = ps² + qr × (st + qr)/2²

pr² = pt² + tr²

pr² = pt² + (sr + st)²

sr = qr/2

=> pr² = pt² + (qr/2 + st)²    Eq1

pt² = ps² - st²

putting in eq 1

pr² = ps² - st² + (qr/2 + st)²

=> pr² = ps² + (qr/2 + st)² - st²

using a² - b² = (a+b)(a-b)

a = qr/2 + st  and b = st

a+b = (qr +st)/2  and a-b = qr/2

=> pr² = ps² + (qr +st)/2 × qr/2

=> pr² = ps² + qr × (qr +st)/4

=> pr² = ps² + qr × (st + qr)/2²

QED

Answer 2

Answer:

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