Saket purchased a rectangular plot having area 200 m.2Legth of plot was 10m more than its breadth. find the length and breadth of the plot.
Answers
Answer:
Length = 20 m
Breadth = 10 m
Step-by-step explanation:
Hey!!
Okay, here we are given the area of the rectangular plot, i.e., 200 m².
And there is one condition. Well, this condition says that the length is 10 m more than the breadth. So, arithmetically we can say, l = b + 10 m.
Okay, so let's put the above equation in the formula of the area...
Area of Rectangle = l × b
= (b + 10) × b
= b² +10b
200 m² = b² + 10b m
⇒ b² + 10b -200 = 0
Now, here we got a quadratic equation, well, that'll take a bit of time... hmm.. so let's use the factorize method to find the value of b.
b² + 10b -200 = 0
We can write the above equation as;
(b² - 10b) + (20b - 200) = 0
⇒ (b - 10) (b + 20) = 0
Using the Zero Factor Principle;
b = 10, -20
Here, we got two values of b, well, you may know that the length of anything cannot be negative. So, the value of b is 10 m.
With the value of b we can find the value of a, i.e., a = b + 10 = 10 + 10 = 20 m.
Therefore, the length and breadth of the rectangular plot are 20 m and 10 m respectively. :)
Hope you got the answer!! :)
Question:
Saketh purchased a rectangular plot having area 200 m². Length of plot is 10m more than its breadth. Find the length and breadth of the plot.
Solution:
We know that, area of the rectangular plot Saketh purchased is 200m².
Also given, the length of the rectangular plot is 10m more than the breadth.
So, we can conclude l = b + 10.
Area of the plot= l × b
= (b + 10) × b
= b² + 10b
The equation is 200m² = b² + 10b
b² + 10b -200 = 0
Factorizing, this expression, we get;
(b² - 10b) + (20b - 200) = 0
(b - 10) (b + 20) = 0
Therefore, b = 10, -20 (by transposition)
Since distances cannot be expressed in negative values, the breadth of the rectangular plot is 10m and length of the rectangular plot is 10m more than its breadth which is 10m + 10m = 20m.
Therefore, breadth = 10m and length = 20m.