In parallelogram DEFG, DH = x…

Maths Questions

In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x – 4, and HE = 5y + 1. Find the values of x and y. Note that the diagram is not drawn to scale.

Answer

Final answer: Solving the equations based on the properties of parallelograms leads us to the values of x and y, which are 2.5 and -0.5, respectively. Explanation: The task requires finding the values of x and y in parallelogram DEFG. We know that DH = x + 1, HF = 3y, GH = 3x – 4, and HE = 5y + 1. Utilizing the properties of a parallelogram, where opposite sides are equal, allows us to establish equations: DH = GH and HF = HE. Therefore, we can create the equations: x + 1 = 3x – 4 and 3y = 5y + 1. To find x, we rearrange the first equation: x + 1 = 3x – 4 implies 5 = 2x, resulting in x = 2.5. For y, we rearrange the second equation: 3y = 5y + 1 leads to -1 = 2y, thus y = -0.5. Consequently, the values that fulfill the requirements of parallelogram DEFG are x = 2.5 and y = -0.5.

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