Q10 of 45 Page 43

Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was 15 km. Find their speed per hour.


Let their speed be 'x' km/h


We know, distance = speed × time


In two hours,


Distance travelled by both = '2x' km


Let their starting point be 'O', and Pranali and Prasad reach the point A in the East and point B in the north direction respectively.


Clearly, AOB is a right-angled triangle, So By Pythagoras theorem


(Hypotenuse)2 = (base)2 + (Perpendicular)2


(AB)2 = (OA)2 + (OB)2


As, AB = distance between them = 15√2 km


And OA = OB = distance travelled by each = 2x


⇒ (15√2)2 = (2x)2 + (2x)2


⇒ 450 = 8x2


⇒ x2 = 56.25


⇒ x = 7.5 km/h


More from this chapter

All 45 →
8

From the information given in the figure 2.31, prove that PM = PN =


9

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

 11

In seg BL and seg CM are medians of ∆ ABC. Then prove that : 4(BL2 + CM2) = 5 BC2


 12

Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is14 cm. Find the length of the other diagonal.