Practice the questions given in the worksheet on Pythagorean Theorem. We know, in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of its remaining two sides.

Hypotenuse\(^{2}\) = Perpendicular\(^{2}\) + Base\(^{2}\)

**1.** The side of the triangle are of length 7.5 m, 4 m, 8.5 m. Is this triangle a right triangle? If so, which side is the hypotenuse?

**2.** In ∆ABC right angled at A. if AB = 10 m and BC = 26 m, then find the length of AC.

**3.** In ∆XYZ right angled at Y. find the length of the hypotenuse if the length of the other two sides is 1.6 cm and 6.3 cm.

**4.** If the square of the hypotenuse of an isosceles right triangle is 98cm\(^{2}\), find the length of each side.

**5.** A tree broke from a point
but did not separate. Its top touched the ground at a distance of 24 m from its
base. If the point where it broke is at the height of 7 m from the ground, what
is the total height of the tree?

**6.** A ladder 13 m long when set
against the wall of house just reaches a window at a height of 12 m from the
ground. How far is the lower end of the ladder from the base of the wall?

**7.** Find the perimeter of the
rectangle whose length is 24 cm and diagonal is 26 cm.

**8.** The diagonal of the rhombus
is 24 m and 10 m. find the perimeter.

**9.** One of the diagonals of the
rhombus is 3 cm and each side is 2.5 cm. Find the length of the other diagonal
of the rhombus.

**10.** A ladder 8.5 m long rests
against a vertical wall with its foot 4 m away from the wall. How high up the
wall the ladder reach?

**11.** The height of two towers is
150 m and 136 m respectively. If the distance between them is 48 m, find the
distance between their tops.

**12.** The base of an isosceles
triangle is 24 cm and the two equal sides are 37 cm each. Find the altitude AD
of the triangle.

**13.** ∆PQR is an isosceles right
triangle right angled at R. Prove that PQ\(^{2}\) = 2PR\(^{2}\).

**14.** Starting from a place, two
person travel in bicycles along two perpendicular roads at speed of ** u** km/hr and

Answers for the worksheet on Pythagorean Theorem are given below to check the exact answers of the above questions on Pythagoras.

**Answers:**

**1.** Yes, hypotenuse = 8.5 m

**2.** 24 m

**3.** 6.5 cm

**4.** 7 cm

**5.** 32 m

**6.** 5 m

**7.** 68 cm

**8.** 52 m

**9.** 4 cm

**10.** 7.5 m

**11.** 50 m

**12.** 35 cm

**14.** \(t\sqrt{u^{2} +
v^{2}}\)

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