If a metal wire 40cm long is bent to form a rectangle, then what are its dimensions when it’s area is maximum?
Answers
Step-by-step explanation:
let the length of the metal wire be a.
therefore a=40cm
since metal wire is cut into two pieces …let the length of two pieces be a1 and a2…so a=a1+a2
now we have to find the area of metal wire before cutting..since it is to be square..length of each side will be 10 cm
hence area of square will be a^2=10*10=100cm^2
therefore a^2=100cm^2=(a1+a2)^2
given that after cutting sum of their areas are 58 cm^2..therefore
a1^2+a2^2=58 cm^2
now we have two equations to solve
1.(a1+a2)^2=100
2.a1^2+a2^2=58
on solving these two..we get a1*a2=21
it easy two find those two numbers because a1 and a2 values can be satisfied bye only two pairs (1,21) and(7,3)
and only (7,3) pair satisfies the condition (a1+a2)^2=100 and also a1^2+a2^2=58..(verification method to find values)..
hence length of the two pieces will be 7cm and 3 cm respectively
Answer:
Dimensions are length=10cm and breadth=10cm