A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side leng
th of the rhombus. A rhombus with diagonals is shown. The diagonals form 4 triangles. All sides are 4 inches long. The distance from the top point to the middle point is 2 inches. The distance from the right point to the middle point is x. One interior angle is 30 degrees and another is a degrees. Which measures are true for the quilt piece? Select three options. a = 60° x = 3 in. The perimeter of the rhombus is 16 inches. The measure of the greater interior angle of the rhombus is 90°. The length of the longer diagonal is approximately 7 inches.
1 answer:
Answer:
1) a = 60°
3) The perimeter of the rhombus is 16 inches.
5) The length of the longer diagonal is approximately 7 inches.
Step-by-step explanation:
From the attached diagram, we begin to compare the options
1)a = 60°
From the question, we are told that:
One interior angle is 30 degrees and another is a degrees
The sum of angles in a rhombus = 360°
There are 4 angles in a rhombus and each angle should normally be equal to 90° hence,
a = 90° - 30°
a = 60°
2) x = 3 in.
Looking at the attached diagram,
We solve for x using Pythagoras Theorem
a² + b² = c²
a = 2 inches
b = x = ??
c = 4 inches
Hence,
2² + b² = 4²
b² = 4² - 2²
b² = 16 - 4
b² = 12
b = √12
b = 3.4641016151 inches
Option 2 is incorrect
3) The perimeter of the rhombus is 16 inches.
A rhombus is a quadrilateral with 4 sides that are equal to each other.
The perimeter of a Rhombus = 4a
Where a = Length of the side of a rhombus
From the above question, we are told that, the length of each side = 4 inches
Hence, perimeter = 4 × 4
= 16 inches.
Option 3 is correct
4)The measure of the greater interior angle of the rhombus is 90°.
The measure of the greater interior angle = 2 × a°
a° has already been solved for in option 1 as 60°
Hence,
Measure of the greater interior angle = 2 × 60°
= 120°
Option 4 is not correct.
5)The length of the longer diagonal is approximately 7 inches.
Since the Rhombus forms 4 equal triangles, it means the diagonals are the same.
Hence, the length of the longer diagonal
= 2 × 3.4641016151
= 6.9282032303 inches
Approximately = 7 inches.
Option 5 is correct.
Hence, the correct options are
1) a = 60°
3) The perimeter of the rhombus is 16 inches. The measure of the greater interior angle of the rhombus is 90°.
5) The length of the longer diagonal is approximately 7 inches.
You might be interested in