Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.



Similarly, we have



Now, to find the lengths of the diagonals,


So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units
R example: 6 1/2 = 13/2 = 6.5
For the first example, six and a half is equal to thirteen halves, which
is then equal to six point five. To do this, the rule to turn a mix
number into a fraction is by multiplying the 2 with the 6 and then add
the answer to 1, which gives 13/2 (Remember to always give the same
denominator). Finally, thirteenth halves is equal to six point five
(because when you divide 13 by 2, you get 6 and one left over. To
continue dividing, add a 0 , and so 10 goes into 2 is five. so the
decimal is 6.5
8<-5x+20 is one possible answer. it depends on how they are writing it. you need to do the distributed property.
Question 1 Answer:
Aunt 1 and Grandma 1 would fill gift bags.
Mom and Aunt 2 would make centerpieces.
You and Grandma 2 would blow up balloons.
Since you are pairing up to complete the tasks, these pairs each have the shortest times in their respective categories and therefore are the most logical pairing to complete tasks.
Question 2 Answer:
We use algebra and our previous pairings to determine the length of each task.
<u>Gifts Bags --> 6/7 hours</u>
x = time together
= rate of completion
Aunt 1 =
Grandma 1 =

<u>Centerpieces --> 7/4 hours</u>
x = time together
= rate of completion
Mom =
Aunt 2 = 



<u>Balloons --> 15/16 hours</u>
x = time together
= rate of completion
You =
Grandma 2 = 



Shortest amount of time to complete all tasks is:
≈ 3.54 hours
Converting hours to hours and minutes --> 3 hours 32 minutes
Therefore they must arrive by 5:28pm to complete the tasks in time to leave at 9:00pm.
X(a+b)-y(a+b)
*factor out (a+b)*
=(a+b)(x-y)