SOLUTION: What are the length and width of a rectangle that has a perimeter of 98 cm and a diagonal of 35 cm?

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Question 18728: What are the length and width of a rectangle that has a perimeter of 98 cm and a diagonal of 35 cm?
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
perimeter=2(a+b)=98 cm
2(a+b)=98
a+b=49
b=(49-a)....[1]
diagonal=sqrt(a^2+b^2)=35 cm
sqrt(a^2+b^2)=35....[2]


Now from eqn two,
sqrt(a^2+b^2)=35
(a^2+b^2)=(35)^2
(a^2+b^2)=1225
Now from eqn one,
b=(49-a)
b^2=(49-a)^2
Substituting this we get,
(a^2+b^2)=1225
a^2+(49-a)^2=1225
a^2+(2401+a^2-98a)=1225
2a^2-98a+2401=1225
2a^2-98a+2401-1225=0
2a^2-98a+1176=0
a^2-49a+588=0
(a-28)(a-21)=0
a=28,21
b=49-a=21,28


so we get the dimensions as:
{21,28}cm or {28,21}cm


hope this helps,
Prabhat