geometry

 

Two sides of a parallelogram are 30 and 20.     

One diagonal has a length of 40.     

What is the length of the other diagonal?      

 

 The Parallelogram Law states that the sum of the squares of     

 the diagonals equals the sum of the squares of the four sides.     

 

 (d₁² + d₂²)  =  2 • (a² + b²)     

 d₁² + 40²  =  2 • (30² + 20²)     

 d₁² + 1600  =  2 • (900 + 400)     

 d₁²  =  1800 + 800 – 1600     

 d₁²  =  1000     

 d₁  =  sqrt(1000)     

 d₁  =  10 • sqrt(10)     —>>  about 31.62     

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