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PLS HELP
PYTHAGOREAN THEOREM

PLS HELP PYTHAGOREAN THEOREM class=

Sagot :

Knightx227
A^2+B^2=C^2 or the length of the 2 shortest sides squared equals the longest leg squared
sqdancefan

Answer:

  8.  20.8 units

  9.  isosceles

Step-by-step explanation:

8.

The vertical altitude line divides the triangle into two congruent right triangles. Each has a horizontal leg of 4 units, and a vertical leg of 5 units. (You can find these lengths by subtracting coordinates, or by counting grid squares.)

slant sides

The hpotenuses of these right triangles are the short sides (PR, QR) of the larger triangle PQR. We can find their length using the Pythagorean theorem. Defining S as point (-2, -1), we have ...

  PS² +SR² = PR² . . . . . . . . . . . . the Pythagorean theorem relation

  4² +5² = PR² = 16 +25 = 41 . . . with numbers filled in

  PR = √41 . . . . . . . . . . . . . . take the square root

  PR ≈ 6.4 . . . . . . . . . . . round to tenths

horizontal side

The length of side PQ is 8 units, found by subtracting x coordinates ((2 -(-6)) = 8), by counting grid squares, or by doubling the length of PS (2(4) = 8).

perimeter

The perimeter of the triangle is the sum of its side lengths:

  perimter = PR +QR +PQ = 6.4 +6.4 +8 = 20.8

The perimter of triangle PQR is 20.8 units.

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9.

Sides PR and QR are congruent, so the triangle is isosceles.

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Additional comment

A triangle whose vertices are integer grid coordinates cannot be equilateral.

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