Quiz-1

When the length of the ladder =  20 m

then the length  of the shadow = 10 m i.e; in this case

length = 2 x shadow

With the same angle of inclination of the sun , the length of tower that casts a shadow of 50 m will be

2 x 50 = 100 m

i.e; the height of the tower is 100 m

(Ratio of corresponding heights)2 = Ratio of area of similar trianges

Ratio of corresponding heights  in this question = √(16/25) = 4/5

3 x (Sum of squares of the sides of the triangle) = 4 x (Sum of squares of the medians of the triangle)

(3/4) x (6² x 7² x 8²) = Sum of square of the medians

= (3/4) x 149 = 111.75 cm²

Area of trapezium =1/2 ×(sumof parallel sides) ×(distance between them )

1/ 2 (20+18) x 15

=285 cm2

6 , 8 and 10 form a pythagorean triplet, thus this triangle is a right angle triangle

the measure of inradius of a right angle triangle = (Sum of legs of the triangle - Hypotenuse)/2

= ((6+8)-10)/2

= 2

Solution: Given: radius of circle=21 cm
Central angle=135°
To find: Perimeter of sector.
Firstly we have to find the length of arc.
So length of arc = theta/ 360°×2pi R
= 135°/360°×2×22/7 × 21
= 27°/72° × 44×3
= 9°/24° × 44×3
= 9/6×44
= 3/2× 44
= 3 × 22= 66 cm
Now, Perimeter of sector= 2×r + length of arc
= 2×21+ 66
= 42+66
= 108 cm

 

Number of quadilaterals can be formed = 8C4 = 70

Number of triangles that can be formed = 8C3 = 56

Requiered difference = 70-56 = 14

Since we are given a measure of 19º angle, if we use the measure 19 times we would be able to measure 361º and hence, we can measure 361º and hence, we can measure 361-360 = 1º. Hence, it would be possible to divide the circle into 360 equal parts

Let AB = a³, AC = 3ⁿ according to the question :

3ⁿ = 3.a³ or

a³ = 3^n-1

perimeter P = 397 + 3ⁿ + 3^n-1

P - 397 = 3^n-1[3+1] = 4.3^n-1

Thus p - 397 should be a multiple of both 3 and 4 only option (d) p = 3313 feet satisfies this condition, so option (d) is correct