MENSURATION
SESSION – 14.1
Q 1 ] . The side of a square exceeds the side of another square by 5cm and the sum of the areas of two squares is 325 cm 2 . Find the side of each square .
SOLUTION :
Let the side of the 2nd square = x cm
Thus , the side of the 1st square = (x + 5 ) cm
Area of the 1st square = S * S = ( x + 5 )2 cm2
Area of the 2nd square = S * S = x2 cm2
Given : –
Sum of the areas of two squares = 325 cm2
According to the problem ,
(x + 5 )2 + x2 = 325
x2 + 10x + 25 + x2 = 325
2x2 + 10x + 25 – 325 = 0
2x2 + 10x – 300 = 0
2 ( x2 + 5x – 150 ) = 0
x2 + 5x – 150 = 0/2
x2 + 5x – 150 —( Factorize the middle term )
x2 + 15x – 10x -150 = 0
x(x + 15 ) – 10 ( x + 15 ) = 0
(x + 15 ) (x – 10 ) = 0
x + 15 = 0 or x – 10 = 0
x = – 15 or x = 10
Value of side of a square can not be negative . (-15)
Therefore , x = 10 is the side of 2nd square = 10cm
Side of the 1st square = (x + 5 ) = 10 + 5 = 15cm .
————————————————————————-
Q 2] . There is a square of side 44cm . Find the radius of the circle whose perimeter is equal to the perimeter of the square .
SOLUTION :
Given : – Side of a square = 44cm
Thus , Perimeter (circumference ) of a circle = Perimeter of the square
Find : Radius of the circle = ?
Side of the square = 44cm
Thus, perimeter of square = 4 * S = 4 * 44 = 176cm
Since , Perimeter of circle = Perimeter of square = 176 cm
Thus , P ( circumference of a circle ) = 176
2pie * r = 176
2 * 22/7 * r = 176
thus , r = 176 * 1/2 * 7/22 = 28cm = r
Therefore , the radius of the circle is = 28 cm
———————————————————————————————————
Q 3] . A rectangular floor of dimensions 8.4m x 5.4m is to be tiled with right – triangular marble pieces , with base 40cm and height 30cm . How many marble pieces will be required to cover the floor .
SOLUTION :
RECTANGULAR FLOOR
L = 8.4 m
B = 5.4 m
Area of floor = L * B
= 8.4 x 5.4
45 .36 m2
RIGHT TRIANGULAR TILES
B = 40 cm
H = 30 cm
AREA OF TRIANGLE = 1/2 x B x H
= 1/2 x 40 x 30
= 600 cm2
= 600/100 = 6m2
Number of marble pieces tiles required to cover the floor = ?
Number of tiles = Area of floor = 45.36 = 4536 = 756 tiles .
—————– ——- ——-
Area of right 6 60
triangular tiles
————————————————————————————————————————–
Q 4 ] . The hour hand of a clock is 6.3 cm long . Find the distance covered by it in 2 days .
SOLUTION :
Length of the hour hand of a clock = 6.3cm
Therefore , radius of a circle = 6.3cm
The hour hand takes 2 rounds of the clock to cover a day .
Thus to cover 2 days it will take = 4hrs
Distance covered by an hour hand in 2 days = ?
Distance covered by an hour hand in one round = Circumference of a circle = ?
Circle of a circle = 2pie * r = 2 x 3.14 x 6.3 = 39.6 cm
1 Round ( perimeter ) = 39.6cm
4 rounds = ?
= 39.6 x 4 = 158.4cm
Distance covered by hour hand in 2 days = 158.4cm
—————————————————————————————————————