# James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagonal: 20 in.

###### Question:

## Answers

The correct options are options 1 and 4.

The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 1 do not form right angles.

The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 4 do not form right angles.

Step-by-step explanation: When you have the dimensions of a quadrilateral given along with the diagonal (which is also the hypotenuse) you basically have the quadrilateral divided into two triangles. You can determine if the triangles are going to be right angled or not simply by using the Pythagoras theorem as a test.

Note also that if the angles are right angled, then the quadrilaterals can all be conveniently placed, one in each quarter of the circle without overlapping. This is possible because each quarter of a circle measures 90 degrees.

To test if the angles formed are right angled we shall take the following steps;

Pythagoras theorem states that; AC² = AB² + BC²

Where AC is the longest side (hypotenuse), and AB and BC are the other two sides.

(Quad 1) > 20² = 12² + 15²

400 = 144 + 225

400 ≠ 369

Both sides pf the equation are not equal, hence the vertices of parallelogram 1 do not form a right angle.

(Quad 2)> 34² = 16² + 30²

1156 = 256 + 900

1156 = 1156

Both sides of the equation are equal, hence the vertices of parallelogram 2 forms a right angle

(Quad 3)> 29² = 20² + 21²

841 = 400 + 441

841 = 841

Both sides of the equation are equal, hence the vertices of parallelogram 3 forms a right angle

(Quad 4)> 26² = 18² + 20²

676 = 324 + 400

676 ≠ 724

Both sides sides of the equation are not equal, hence the vertices of parallelogram 4 do not form a right angle.

From the results shown above, if the four parallelograms are placed in each of the four corners of the circle, they would definitely overlap because two of them do not form right angles at their vertices.

The correct options are;

*The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 1 do not form right angles

**The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 4 do not form right angles.

Step-by-step explanation: What James is trying to do is quite simple which is, he wants to place four quadrilaterals inside a circle and he wants the vertices to touch one another at the center of the circle without having to overlap.

This is possible and quite simple, provided all the quadrilaterals have right angles (90 degrees). This is because the center of the circle measures 360 degrees and we can only have four vertices placed there without overlapping only if they all measure 90 degrees each (that is, 90 times 4 equals 360).

We can now show whether or not all four parallelograms have right angles by applying the Pythagoras' theorem to each of them. Note that James has cut the shapes in such a way that the hypotenuse (diagonal) and the other two legs have already been given in the question. As a reminder, the Pythagoras' theorem is given as,

AC² = AB² + BC² Where AC is the hypotenuse (diagonal) and AB and BC are the other two legs. The experiment would now be as follows;

Quadrilateral 1;

20² = 12² + 15²

400 = 144 + 225

400 ≠ 369

Therefore the vertices of parallelogram 1 do not form a right angle

Quadrilateral 2;

34² = 16² + 30²

1156 = 256 + 900

1156 = 1156

Therefore the vertices of parallelogram 2 forms a right angle

Quadrilateral 3;

29² = 20² + 21²

841 = 400 + 441

841 = 841

Therefore the vertices of parallelogram 3 forms a right angle

Quadrilateral 4;

26² = 18² + 20²

676 = 324 + 400

676 ≠ 724

Therefore the vertices of parallelogram 4 do not form a right angle

The results above shows that only two of the parallelograms cut out have right angles (like a proper square or rectangle for instance), while the other two do not have right angles.

Therefore, the correct option are as follows;

The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 1 do not form right angles.

The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 4 do not form right angles.

B and E

Step-by-step explanation:

B. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.

E. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

Step-by-step explanation:

hope it helps:3

B and E

Step-by-step explanation:

The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.

The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

B. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.

E. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

Step-by-step explanation:

P1: 12^2+15^2=20^2 144+225=400 369=400

P2: 16^2+30^2=34^2 256+900=1156 1156=1156

P3: 20^2+21^2=29^2 400+441=841 841=841

P4: 18^2+20^2=26^2 324+400=676 724=676

So the answers are B and E

the answer is b and e

Step-by-step explanation:

Quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

hope this : )