Question

1. In a right angled triangle, find the length of the hypotenuse, if the other two sides measure
2. The length of one side of a right triangle is 24 cm and the length of its hypotenuse is 40 cm. Fin
3. The two legs of a right triangle are equal and the square of its hypotenuse is 50 cm. Find te
12 cm and 35 cm.
the length of its third side.
A
C
length of each leg.
4. Given below are the lengths of the legs of right AABC. In each case, find the length
of the hypotenuse of AABC :
(i) a = 32 cm, b = 60 cm
(ii) a = 28 m, b = 45 m
(iii) a = 32 cm, b = 24 cm
5. Given below are the lengths of the sides of AABC. In each case, state whether AABC is right ar
с
а
or not:
(i) AB = 40 cm, BC = 58 cm, CA = 44 cm
(ii) AB = 43 cm, BC = 35 cm, CA = 12 cm
(iii) AB = 55 cm, BC = 73 cm, CA = 48 cm
6. A man travels 90 km due East and then 56 km due South. How far is he from the starting
7. A long pole is made to stand against a wall in such a way that its foot is 16 m from the w
its top reaches a window 12 m above the ground. Find the length of the pole.
8. Find the length of the diagonal of a rectangle whose sides are 21 cm and 20 cm.
9. Fill in the blanks:
(i) In a right triangle, the square of the hypotenuse is equal to the of the squa
the other two sides.
(ii) If the square of one side of a triangle is equal to the sum of the squares of the othe
sides, then the triangle is ........
(iii) Of all the line segments that can be drawn to a given line from a given point outsi
is the shortest.
......​

Answer 1

Answer:

2.According to Pythagoreas theorem,

(perpendicular)^2+ (base)^2 = (hypotenuse)^2

(24)^2+x^2=(40)^2

576+x^2 = 1600

x^2=1024

x=32cm

4.(i) (32)^2+(60)^2

(x)^2=1024+3600

       =4624

      x=68cm

(ii)(28)^2+(45)^2

(x)^2=784+2025

(x)^2=2809

x=53m

(iii)(32)^2+(24)^2

x^2=1024+576

x^2=1600

x=40cm

5.(i) no

(ii)no

(iii)yes

6.(90)^2+(56)^2=x^2

x^2=11236

x=106km