Question

A quilt 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? 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.

Answer 1

The following measures are true for the quilt:

1. a = 60°

3. The perimeter of the rhombus is 16 inches.

5. The length of the longer diagonal is approximately 7 inches.

I have attached the picture describing the rhombus.

One by one we will check all the options:

As we can see that:

a+30°=90°

a = 90-30

1) a= 60° which is true

Taking the triangle with the perpendicular x, and using Pythagoras theorem, we get:

$perp^{2}+base^{2} =hyp^{2}$

$x^{2} +2^{2} =4^{2}$

$x^{2} =16-4$

x = 12

x = 2$\sqrt{3}$ = 3.46 ≠ 3

So option 2, is not true.

Perimeter of rhombus= 4 x 4 = 16 inches

So option 3 is correct

Smaller Interior angles of rhombus = 30+30= 60°

Measure of greater interior angle of rhombus = a + a=60 + 60 = 120°

So Option 4 is incorrect

The length of the longer diagonal is the horizontal diagonal which is:

x + x= 2x

2x = 2(3.46) = 6.92 ≈ 7

So Option 5 is correct

Therefore,

The following measures are true for the quilt:

1. a = 60°

3. The perimeter of the rhombus is 16 inches.

5. The length of the longer diagonal is approximately 7 inches.

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