SOLUTION: the perimeter of a rectangular picture is 34 cm and the diagonal is 13 cm. find the dimensions of the picture.

Question 121640: the perimeter of a rectangular picture is 34 cm and the diagonal is 13 cm. find the dimensions of the picture.
Found 2 solutions by checkley71, oscargut:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
13^2=a^2+b^2 where 34/2=17 or a+b=17 or a=17-b
13^2=(17-b)^2+b^2
169=289-34b+b^2+b^2
2b^2-34b+289-169=0
2b^2-34b+120=0
2(b^2-17b+60)=0
2(b-12)(b-5)=0
b-12=0
b=12 one side
b-5=0
b=5 the other side.
proof
2*12+2*5=34
24+10=34
34=34
12^2+5^2=13^2
144+25=169
1169=169

Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
Let a and b the sides of the rectangular picture
then 2(a+b)=34 then
a+b=17
and using the diagonal is 13 and pitagoras then
a^2+b^2=13^2
a^2+(17-a)^2=169
cms
a^2+289-34a+a^2=169
2a^2-34a+120=0
a^2-17a+60=0
the solution to this equation a=12 and a=5 then
the dimensions are 12 and 5 cms

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