Q39 of 186 Page 4

The length of a room exceeds its breadth by 3 metres. If the length is increased by 3 metres and the breadth is decreased by 2 metres, the area remains the same. Find the length and the breadth of the room.

Let the breadth of a room = x m

According to the question,


Length of the room = x + 3


Then, Area of room = (x + 3)× (x) m2


= x2 + 3x


Condition II:


Area remains same,


when length = (x + 3 + 3) m = (x + 6) m


and breadth = (x – 2) m


According to the question,


x2 + 3x = (x + 6)(x – 2)


⇒ x2 + 3x = x2 – 2x + 6x – 12


⇒ 3x = 4x – 12


⇒ 3x – 4x = – 12


⇒ x = 12


So, length of the room = (x + 3) = 12 + 3 = 15m


Hence, the length of the room is 15m and the breadth of a room is 12m


More from this chapter

All 186 →
37

In a ΔABC, ∠A = x°, ∠B = (3x)° and ∠C = y°.

If 3y — 5x = 30, show that the triangle is right – angled.

 38

The area of a rectangle gets reduced by 8 m2, when its length is reduced by 5m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m2. Find the length and the breadth of the rectangle.

 40

Two places A and B are 120 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 6 hours, and if they move in opposite directions, they meet in 1 hour 12 minutes. Find the speed of each car.

 41

A train travels a distance of 300 km at a constant speed. If the speed of SE the 2O train is increased by 5 km an hour, the journey would have taken 2 hours less. Find the original speed of the train.