Question

Given that the side length of a rhombus is the geometric
mean of the lengths of its diagonals. The degree measure
of the acute angle of the rhombus is
(1) 15
(2) 30°
(3)45
(4)60​

Answer 1

Answer:

option (2) is the right answer

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Step-by-step explanation:

Answer 2

Answer:

The degree measure of the acute angle of the rhombus is 30 degree

Step-by-step explanation:

Geometric mean

x = √ab

$x^{2} = ab$      (1)

Area of rhombus = $2 * \frac{1}{2}x^{2} sin$θ

= $x^{2} sin$θ   (2)

Area of rhombus = $\frac{ab}{2}$      (3)

Equate the equation 2  and 3

$x^{2} sin$θ  = $\frac{ab}{2}$

$2x^{2} sin$θ  = ab    (4)

Equate equation 1 and 4

$2x^{2} sin$θ  = $x^{2}$

$x^{2}$(2sinθ  - 1) = 0

2sinθ - 1 = 0

2sinθ = 1

sinθ = 1/2

sinθ= $30^{0}$

Final answer:

The degree measure of the acute angle of the rhombus is 30 degree

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