Converse of Pythagoras Theorem

Q.

If $x+\frac{1}{x}=\sqrt{3}$, then $x$ equal:

1. $\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}$

2. $\cos \frac{\pi }{2}+i\sin \frac{\pi }{2}$

3. $\sin \frac{\pi }{6}+i\cos \frac{\pi }{6}$

4. $\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}$

Q. The sides of a triangle are of lengths 8 cm, 15 cm and 17 cm. The triangle is a right-angled triangle.

1. True
2. False

Q. The sides of a triangle are of lengths 4.5 cm, 6 cm and 7.5 cm. The triangle is a right-angled triangle.

1. True
2. False

Q.

The hypotenuse of a right triangle with its legs of lengths $3x\times 4x$ is

1. $5x$

2. $7x$

3. $16x$

4. $25x$

Q. Prove that the area of the semi-circle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semi-circles drawn on the other two sides of the triangle.

Q. The measure of $\angle B$ in the given triangle (in degrees) is ___.

1. ${50}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${40}^{\circ }$

Q. In a right-angled triangle, the length of the largest side is 10cm and that of another side is 8cm. Then the length of the third side is equal to

1. 6cm
2. 4cm
3. 12cm
4. 7cm

Q. △PQR has three sides as PQ = 25 units, QR = 20 units, and PR = 15 units. So, the largest angle in the triangle is .

1. 90°
2. 180°
3. 100°
4. 45°

Q.

Question 127

Solve the following question:

Rahul walks 12 m North from his house and turns West to walk 35 m to reach his friend's house. While returning, he walks diagonally from his friend's house to reach back to his house. What distance did he walk while returning?

Q.

(a) In a marathon, you started from checkpoint A and ran 5 km towards West. The checkpoint you reached was B. Then, you again ran for 12 km towards North and reached checkpoint C. Find the length of the shortest path which you must take to reach the finishing checkpoint A.

(b) Show that the angles of an equilateral triangle are 60° each. [4 MARKS]

Q. Which of the following lengths make a right triangle?

1. $\sqrt{5},3,\sqrt{14}$
2. $6,2\sqrt{3},8$
3. $3\sqrt{2},4\sqrt{2},5\sqrt{2}$
4. $2\sqrt{3},2\sqrt{2},2\sqrt{5}$