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boyakko [2]
2 years ago
9

Need help

Mathematics
2 answers:
s344n2d4d5 [400]2 years ago
8 0
  • A rectangle garden is 50m long and 45 m broad. A path 2m wide is. running inside the garden.
  • Area of the rectangular garden = (50 × 45) square metres = 2250 square metres.
  • Area of the rectangle which is left after the path is paved = [(50-2×2)×(45-2×2)] square metres = [(50-4) × (45-4)] square metres = (46 × 41) square metres = 1886 square metres.
  • Therefore, the area of the path = (2250 - 1886) square metres = 364 square metres.
  • Therefore, the cost of gravelling the path at Rs. 40 per square metre = Rs. (40 × 364) = Rs. 14560.

<u>Answe</u><u>r</u><u>:</u>

<u>Rs.</u><u> </u><u>1</u><u>4</u><u>5</u><u>6</u><u>0</u>

Hope you could get an idea from here.

Doubt clarification - use comment section.

Sliva [168]2 years ago
4 0

In rectangle ABCD

  • L=50m
  • B=45m

\\ \sf{:}\longrightarrow Area=LB

\\ \sf{:}\longrightarrow Area=50(45)

\\ \sf{:}\longrightarrow Area=2250m^2

In rectangle PQRS

  • L=50-2=48m
  • B=45-2=43m

\\ \sf{:}\longrightarrow Area=LB

\\ \sf{:}\longrightarrow Area=48(43)

\\ \sf{:}\longrightarrow Area=2064m^2

Now

\\ \sf{:}\longrightarrow Area_{(Path)}=Area_{(ABCD)}-Area_{(PQRS)}

\\ \sf{:}\longrightarrow Area_{(Path)}=2250-2064=186m^2

Cost:-

\\ \sf{:}\longrightarrow 186(40)

\\ \sf{:}\longrightarrow Rs 7440

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Answer:

 IS a parallelogram

Step-by-step explanation:

The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...

  m = (y2 -y1)/(x2 -x1)

The distance formula for the length of that same line is ...

  d = √((x2 -x1)^2 +(y2 -y1)^2)

Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.

The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)

_____

<em>Additional comments</em>

There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:

  B +D = (-2+6, -9-3) = (4, -12)

  C +E = (0+4, -5-7) = (4, -12)

These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.

__

If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)

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