Solve for x ................
1 answer:
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Answer:
The area of the rhombus is 25.83 cm².
Step-by-step explanation:
The area of a rhombus is given by:
Where:
d₁: is one diagonal
d₂: is the other diagonal = d₁ + 4 cm
We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:
h: hypotenuse of the right triangle
a: one side of the right triangle
b: is the other side of the right triangle
From the above we know that:
h = d₁
We can find d₁ with Pitagoras:
By solving the above quadratic equation for d₁ and taking the positive solution we have:
So, d₂ is:
Now, we can find the area:
Therefore, the area of the rhombus is 25.83 cm².
I hope it helps you!