Question

The area of a hall is 806 sq. ft. Its length is 5 ft greater than its width.
Find the dimensions of the hall.

Answer 1

let the width be = x ft
then length will be = (x + 5) ft

Area of rectangle = length * breadth/width
so
806 = (x + 5)(x)
806 = x^2 + 5x
so we get the quadratic equation
x^2 + 5x - 806 = 0

this will factor out to (x + 31)(x - 26)
so x = - 31 or x = 26

since lengths are never negative, so x = 26 is the acceptable value.
so width = x = 26 ft
and width = x + 5 = 26 + 5 = 31 ft

Answer 2

@Happysoul wait l thought area of a rect is l*w

Answer 3

yes you are right,

area of rectangle is the product of its length (l) and its width (w) i.e. l*w or lw
I have solved it on that basis only.......☺

Answer 4

@HappySoul can you help me with this one The area of a hall is 806 sq. ft. Its length is 5 ft greater than its width.
Find the dimensions of the hall.

Answer 5

sorry not that one

Answer 6

I have given the solution above......This is the same question.....

Answer 7

It took a motorboat 1 hour longer to travel 84 miles against the current than travel the same distance with the current.
The speed of the current is 1 mph.
What is the speed of the motorboat in still water?

Answer 8

****In such questions, you have to add the speed of the current to the speed of boat while going downstream and subtract while going upstream****

let the speed of motorboat in still water = x mph
then when it goes down the stream, its speed will be = (x+1) mph
and speed while going up the stream will be = (x - 1) mph

distance in both cases is 84 miles

let the time while going downstream be = T1
and time while going upstream be = T2

Time = distance/speed

so
84 84
T1= ----- and T2 = ------
x+1 x-1

according to the question the boat takes 1 more hour while going upstream (against the current)

so
T2 = T1 + 1

84 84
----- = ----- + 1
x - 1 x +1

84 84 + (x + 1)
----- = -------------
x - 1 (x + 1)

84 85 + x
----- = --------
x - 1 (x + 1)

cross multiplying

84(x + 1) = (85 + x)(x - 1)

simplify this to get a quadratic equation and solve it to get your answer