Question

a
EFGH is a rhombus. Given EG = 22 and FH = 20, what is the length of one side of the rhombus?
Please help :/

Answer 1

Applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

Recall:

• The diagonals of a rhombus bisect each other at right angles, thereby forming 4 right triangles.

• Half of a diagonal and half of the other diagonal make up a right triangle.

Thus, given:

• EG = 22 (diagonal)
• FH = 20 (diagonal).

Find the length of one side using Pythagorean theorem as shown below:

$HG = \sqrt{(\frac{1}{2}EG)^2 + (\frac{1}{2}FH)^2 }$

• Substitute

$HG = \sqrt{(\frac{1}{2} \times 22)^2 + (\frac{1}{2} \times 20)^2 } \\\\HG = \sqrt{11^2 + 10^2} \\\\\mathbf{HG = 14.9}$

Therefore, applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

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