Ex 4.3, 5
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Let Length be x
Given that
Perimeter = 80 m
2(Length + Breadth) = 80 m
(Length + Breadth) = 80/2
(x + Breadth) = 40
Breadth = 40 – x
Also, given that
Area = 400 m2
Length × Breadth = 400
x (40 – x) = 400
40x – x2 = 400
40x – x2 – 400 = 0
0 = – 40x + x2 + 400
x2 – 40x + 400 = 0
We factorize by
splitting the middle term
x2 – 20x – 20x + 400 = 0
x (x – 20) – 20(x – 20) = 0
(x – 20) (x – 20) = 0
x – 20 = 0
x = 20
x – 20 = 0
x = 20
Splitting the middle term method
We need to find two numbers whose
Sum = – 40
Product = 400 × 1 = 400
So, the roots of the equation are 20, and 20
∴ x = 20 is the solution
Therefore,
Length = x = 20 m
Breadth = 40 – x = 40 – 20 = 20 m

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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