Q9 of 45 Page 38

In the figure 2.22, M is themidpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2

In ∆PRQ, ∠PRQ = 900


PQ2 = PR2 + QR2 – – – 1


In ∆PRM, ∠PRM = 900


PM2 = PR2 + MR2


⇒ PM2 = PR2 + 2 [ M is midpoint]


⇒ 4(PM2 – PR2) = QR2 – – – 2


1 And 2 implies


PQ2 = PR2 + 4(PM2 – PR2)


⇒ PQ2 = 4PM2 – 3PR2


PROVED.


More from this chapter

All 45 →
7

In figure 2.21, ∠DEF = 90°, FG ⊥ ED, If GD = 8, FG = 12,find (1) EG (2) FD and (3) EF

 8

Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

 10

Walls of two buildings on either side of a street are parellel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street , its top touches the window of the other building at a height 4.2 m. Find the width of the street.

 1

In ΔPQR, point S is the midpoint of side QR. If PQ = 11,PR = 17, PS = 13,find QR.