What's the length of QR?
1 answer:
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Answer:
Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.
Step-by-step explanation:
Given, the volume of the box, V = 180 feet cube
Let the height of the box, h = x feet
Therefore, length is, l = ( 9+x ) feet
And width is, b = ( x-4) feet
so volume of the box is
V = l x b x h
Factorizing we get
(x+5)(x-6)(x+6)=0
Therefore,
x = -5, -6, 6
Now since the height of the box cannot be negative, so taking the positive value of x, we get
Height of the box, h = x = 6 feet
Length , l = ( 9+x ) = 9+6 = 15 feet
Width , b = ( x-4) = 6-4 = 2 feet
<h3>Answer: Rhombus</h3>
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Reason:
Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.
Segment AB is exactly units long, which is approximately 4.1231 units.
If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.
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Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.
Let's find the slope of AB.
Segment AB has a slope of 1/4.
Do the same for BC
Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.
We don't have perpendicular lines, so the interior angles are not 90 degrees each.
Therefore, this figure is not a rectangle and by extension it's not a square either.
The best description for this figure is a <u>rhombus</u>.