Maharashtra State Board 10th Maths (Part II) Chapter 2 - Pythagoras Theorem

Identify, with reason, which of the following are Pythagorean triplets.

(i) (3, 5, 4)
(ii) (4, 9, 12)

(v) (10, 24, 27)
(vi) (11, 60, 61)

In figure 2.17, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9,QP = 4, find NQ.

In figure 2.18, ∠QPR = 90°, seg PM ⊥ seg QR and Q – M – R,PM = 10, QM = 8, find QR.

See figure 2.19. Find RP and PSusing the information given in ΔPSR.

Ans. RP = 12, PS = 6√3

For finding AB and BC with the help of information given in figure 2.20, complete following activity.

Find the side and perimeter of a square whose diagonal is 10 cm.

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

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

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

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.