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parallelogram DEFG, DH = x + 3, HF = 3y, GH = 2x – 5, and HE = 5y + 2. Find the values of x and y.


x = 36, y = 13


x = 14, y = 39


x = 13, y = 36


x = 39, y = 14

parallelogram DEFG DH x 3 HF 3y GH 2x 5 and HE 5y 2 Find the values of x and y x 36 y 13 x 14 y 39 x 13 y 36 x 39 y 14 class=

Respuesta :

baabaagreysheep
Your answer is x = 36, y = 13.

We can find this by first realising that DH = HF, and GH = HE, as they are both diagonals of the parallelogram. This allows us to write the equations:

2x - 5 = 5y + 2
x + 3 = 3y

If we rearrange the equation x + 3 = 3y into x = 3y - 3, we can see that this becomes a pair of simultaneous equations that we can solve with substitution. Then we can substitute 3y - 3 into the first equation and solve for y:

2(3y - 3) - 5 = 5y + 2
6y - 6 - 5 = 5y + 2
6y - 11 = 5y + 2
- 5y
y - 11 = 2
+ 11
y = 13

Now because we know that x = 3y - 3, we can substitute 13 into this equation:

x = 3(13) - 3
x = 39 - 3
x = 36

I hope this helps!

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