3. Represent the following situations in the form of quadratic equations :
(i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one
more than twice its breadth. We need to find the length and breadth of the plot.
(i) The product of two consecutive positive integers is 306. We need to find the
integers.
(iii) Vinay's mother is 26 years older than him. The product of their ages (in years)
3 years from now will be 360. We would like to find Vinay's present age.
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8
km/h less, then it would have taken 3 hours more to cover the same distance.
We need to find the speed of the train.
Answers
Answer:
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Step-by-step explanation:
thku brother for wishing me
ANSWER
i)
Let the breadth be x m and the length will be 2x+1 m.
Area =l×b
Area =x(2x+1)=528
2x
2
+x−528=0
2x
2
+33x−32x−528=0
⇒2x(x−16)+33(x−16)=0
⇒(2x+33)(x−16)=0
⇒x=16,
2
33
Breadth =16 m and length =33 m
ii)
Let one number be x then the next number will be x+1
x(x+1)=306
⇒x
2
+x−306=0
⇒x
2
+18x−17x−306=0
⇒x(x+18)−17(x+18)=0
⇒(x+18)(x−17)=0
⇒x=17,−18
The numbers are 17 and 18.
iii)
Let Rohan's present age =x yrs.
Then his mother's present age =x+26 yrs
After 3 yrs
Rohan's age =x+3 yrs
His mother's age =x+29 yrs
(x+3)(x+29)=360
⇒x
2
+32x+87−360=0
⇒x
2
+32x−273=0
⇒x
2
+39x−7x−273=0
⇒x(x+39)−7(x+39)=0
⇒(x+39)(x−7)=0
⇒x=7,−39
So, Rohan's present age =7 yrs.
iv)
Let the speed of the train =x km/hr
(x−8)
480
−
x
480
=3
⇒480x−480x+3840=3x(x−8)
⇒3x
2
−24x−3840=0
⇒x
2
−8x−1280=0
⇒x
2
−40x+32x−1280=0
⇒x(x−40)+32(x−40)=0
⇒(x+32)(x−40)=0
⇒x=40,−32
The speed of the train is 40 km/hr.