Radhika runs along the boundary of a rectangular park at the rate of 12 km/hr and completes one full round in 15 minutes. If the length of the park is 4 times its breadth , the area of the park is?

Let length = a metres and breadth = b metres
Then, 2(a+b)= 46
? (a+b) =23 and ab =120
? Diagonal = ?a² + b²
?(23)²-2 x 120
?289 = 17 m

Area of sector = ( arc length x radius ) / 2 cm²
= (3.5 x 5 ) / 2
= 8.75 cm²

Arc length = 2?r (?° / 360°)
= 2 x (22/7) x 21 x (72° / 360°) cm
= 26.4 cm

Area of the sector = [(22/7) x 12 x 12] x [42°/360°] m²
= 52.8 m²

? ?d-d = 105 cm
? (? -1 ) d = 105 cm
? [(22/7)-1] x d = 105 cm
? d = (7/15) x 105 cm = 49 cm

Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4^th of area of the original triangle .
So area of ? DEF = 36/ 4 = 9 m²

Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)

And from question d + l = 5b
? d = 5b - l ...(2)
? d² = 25b² + l² - 10 x lb
? l²+ b² = 25b² + l² - 10 x lb
? l²+b² = 25b² + l² - 10 x 60
? 24b² = 600
? b = ?25 = 5 m
? l = 60 / b = 60 / 5 = 12 m

We know that area of triangle = ( base x height ) / 2
So area of triangle = (BC x AD) / 2 = (AC x BE) / 2
? (10 x 4.4) / 2 = (11 x h) / 2
? h= (10 x 4.4)/11 = 4 cm

Cross section area = 1/2 x ( a + b ) x d
where a and b are the parallel sides, d is the perpendicular distance between them.
? 1/2 x ( a + b ) x d = 640
? d = (640 x 2) / 16 = 80m

Let the parallel sides be 3a and 5a.
So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.
? 1/2 (3a +5a) x 12 = 384
? 8a = 64
? a =8

? Smaller side = 3x = 3 x 8 = 24 cm.