Mathematics, 17.09.2019 04:30 msdevdev777

Aquilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus.
which measures are true for the quilt piece? check all that apply.
1.a = 60°
2.x = 3 in.
3.the perimeter of the rhombus is 16 inches.
4.the measure of the greater interior angle of the rhombus is 90°.
5.the length of the longer diagonal is approximately 7 inches.

Aquilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonal

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Answer from: DASASDAEDWEDA

True: 1, 3, 5

Step-by-step explanation:

The diagram shows the rhombus with the side length of 4 inches.

Properties:

opposite angles of the rhombus are congruent;diagonals of the rhombus bisect each other;diagonals of the rhombus bisect rhombus angles;diagonals are perpendicular;diagonals divide the rhombus into four congruent right triangles with legs that are halves of diagonals.

Consider right triangle (bottom left right triangle) with the hypotenuse of 4 in and acute angle 30°. In this triangle, leg opposite to the 30° angle is half of hypotenuse and is 2 in. By the Pythagorean theorem,

$x^2+2^2=4^2\\ \\x^2=16-4\\ \\x^2=12\\ \\x=\sqrt{12}=2\sqrt{3}\ in$

So, option 2 is false.

The second acute angle of this triangle has the measure

$a^{\circ}=90^{\circ}-30^{\circ}=60^{\circ}$

So, option 1 is true.

The perimeter of the rhombus is the sum of all sides, so

$P=4+4+4+4=16\ in$

Option 3 is true.

The measures of the rhombuses angles are

$2\cdot 30^{\circ}=60^{\circ}\\ \\2\cdot 60^{\circ}=120^{\circ}$

Thus, option 4 is false.

The length of the longer diagonal is

$2x=2\cdot 2\sqrt{3}\approx 6.9\approx 7\ in$

Option 5 is true.

Answer from: lexybellx3

Options 1, 3 and 5 are correct.

Step-by-step explanation:

Option 1.

In the triangle ABO,

30° + 90° + ∠ABO = 180° [ Since diagonals of rhombus intersect at 90°]

∠ABO = 180 - 120 = 60°

Therefore, m∠a = 60° [Since opposite angles of rhombus are always equal]

Option 1 is correct.

Option 2.

Since AO = OC = x [Diagonals of trapezoid bisect each other]

In the triangle AOB,

x² + 2² = 4² [By Pythagoras theorem]

[By the property of trapezoid diagonal intersect each other at 90°]

x² = 16 - 4

x = √12

x = 2√3

Therefore, option 2 is incorrect.

3. Perimeter of the rhombus = 4 + 4 + 4 + 4 = 12

Option 3 is correct.

4. Measure of greater interior angle is = 2 × 60° = 120°

Therefore, option 4 is incorrect.

5. Longer diagonal of the rhombus = 2

= 2 × (2√3)

= 4√3

= 6.92

≈ 7 inches

Therefore, option 5 is correct .

Aquilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonal

Answer from: Quest

cant open file sorry!

step-by-step explanation:

Answer from: Quest

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x

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Aquilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonal...