SOLUTION: How do I solve this? A rectangle with diagonals of length 20 cm has sides in the ratio 2 : 1. Find the: a perimeter b area of the rectangle. I know the answer but not how

Algebra ->  Pythagorean-theorem -> SOLUTION: How do I solve this? A rectangle with diagonals of length 20 cm has sides in the ratio 2 : 1. Find the: a perimeter b area of the rectangle. I know the answer but not how       Log On


   

Question 951465: How do I solve this?
A rectangle with diagonals of length 20 cm has sides in the ratio 2 : 1. Find the:
a perimeter
b area of the rectangle.
I know the answer but not how to find it.
Please help.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A rectangle with diagonals of length d=20cm has sides in the ratio 2+%3A+1.
diagonal divide a rectangle in two right-angle triangles
so, if sides of a rectangle are a and b then we can write equation
d%5E2=a%5E2%2Bb%5E2
since d=20cm, we have

%2820cm%29%5E2=a%5E2%2Bb%5E2
400cm%5E2=a%5E2%2Bb%5E2
since sides in the ratio 2+%3A+1, we have
a%3Ab=2+%3A+1 =>a=2b..substitute in eq. above
400cm%5E2=%282b%29%5E2%2Bb%5E2.......solve for b
400cm%5E2=4b%5E2%2Bb%5E2
400cm%5E2=5b%5E2
400cm%5E2%2F5=b%5E2
80cm%5E2=b%5E2
b=sqrt%2880cm%5E2%29
b=8.94cm
a=2b=>a=2%2A8.94cm=>a=17.88cm

Find the:
a) perimeter
P=2a%2B2b
P=2%2A17.88cm%2B2%2A8.94cm
P=2%2A17.88cm%2B2%2A8.944271909999159cm
P=35.76cm%2B17.88cm
P=53.64cm
b) area of the rectangle.
A=ab
A=17.88cm%2A8.94cm
A=159.8472cm%5E2