Question

In the figure, PT is the altitude of the triangle PQR in which PQ = 25cm,

PR = 17cm and PT = 15cm. If QR = x cm, calculate QR.​

Answer 1

Step-by-step explanation:

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

(i) (3, 5, 4)

(ii) (4, 9, 12)

(iii) (5, 12, 13)

(iv) (24, 70, 74)

(v) (10, 24, 27)

(vi) (11, 60, 61)

ANSWER:

(i) In the triplet (3, 5, 4),

32 = 9, 52 = 25, 42 = 16 and 9 + 16 = 25

The square of the largest number is equal to the sum of the squares of the other two numbers.

∴ (3, 5, 4) is a pythagorean triplet.

(ii) In the triplet (4, 9, 12),

42 = 16, 92 = 81, 122 = 144 and 16 + 81 = 97 ≠ 144

The square of the largest number is not equal to the sum of the squares of the other two numbers.

∴ (4, 9, 12) is not a pythagorean triplet.

(iii) In the triplet (5, 12, 13),

52 = 25, 122 = 144, 132 = 169 and 25 + 144 = 169

The square of the largest number is equal to the sum of the squares of the other two numbers.

∴ (5, 12, 13) is a pythagorean triplet.

(iv) In the triplet (24, 70, 74),

242 = 576, 702 = 4900, 742 = 5476 and 576 + 4900 = 5476

The square of the largest number is equal to the sum of the squares of the other two numbers.

∴ (24, 70, 74) is a pythagorean triplet.

(v) In the triplet (10, 24, 27),

102 = 100, 242 = 576, 272 = 729 and 100 + 576 = 676 ≠ 729

The square of the largest number is not equal to the sum of the squares of the other two numbers.

∴ (10, 24, 27) is not a pythagorean triplet.

(vi) In the triplet (11, 60, 61),

112 = 121, 602 = 3600, 612 = 3721 and 121 + 3600 = 3721

The square of the largest number is equal to the sum of the squares of the other two numbers.

∴ (11, 60, 61) is a pythagorean triplet.