How to Calculate the Diagonal Length of a Parallelogram?

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SUMMARY

The diagonal length of a parallelogram can be calculated using the given circumferences of the triangles formed by the diagonal. In this discussion, the circumference of each triangle is 6.21 m, and the perimeter of the parallelogram is 7.12 m. By solving the equations 2(a+b) = 7.12 and (a+b) + x = 6.21, where x represents the diagonal length, it is determined that the diagonal measures 2.65 m. This method effectively utilizes basic algebra to derive the diagonal from the known circumferences.

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The diagonal divides the parallelogram into two triangles, each triangle circumference is 6.21 m. The circumference of the parallelogram is 7.12 m. Calculate the diagonal length.
I need tips how to solve this problem.
 
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ZebraGa said:
The diagonal divides the parallelogram into two triangles, each triangle circumference is 6.21 m. The circumference of the parallelogram is 7.12 m. Calculate the diagonal length.
I need tips how to solve this problem.

Circumference is the distance around a circle. Perimeter is the distance around a polygon.

Make a sketch ... solve the system of equations for $\color{red}{x}$
 
skeeter said:
Circumference is the distance around a circle. Perimeter is the distance around a polygon.

Make a sketch ... solve the system of equations for $\color{red}{x}$

Sorry I'm a bit lost, I haven't had math for years, can you explain it a bit further?
 
Using the first equation, solve for the quantity $(a+b)$.

Substitute the value you find for $(a+b)$ into the second equation and solve for the length of the diagonal, $\color{red}{x}$.
 
2(a+b)=7.12
x=3.56

(a+b)+3.56=6.21
x=2.65
Diagonal is 2.65 m?
 
That's correct.
 
ZebraGa said:
2(a+b)=7.12
x=3.56

correction ... (a+b) = 3.56

(a+b)+3.56=6.21

correction ... 3.56 + x = 6.21

x=2.65

ok?
 

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