The Midpoint Of AB Is =M6, 2. One Endpoint Is =A8, 7. Find The Coordinates Of The Other Endpoint, B

Using Pythagoras’s theorem, none of the sides represents a right-angle triangle and the range of values for the third side is 8.4 ≤ x ≤ 10

Pythagoras’s Theorem

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC² = AB² + AC². Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

23) The sides are 103, 41.9 and 62.5

The hypothenuse is 103 and legs of triangle are 41.9 and 62.5

Let’s confirm if this follows Pythagoras’s rule

103 = √[(41.9)² + (62.5)²

103 ≠ 75.2

The values does not represent a right-angle triangle

24) The sides are z + 8, 3z + 5 and 4z – 11

z = 6

The side are 6 + 8, 3(6) + 5 and 4(6) – 11 = 14, 23 and 13

Using Pythagoras’s rule,

23 = √(14² + 13²)

23 ≠ 19.1

The sides does not represent a right angle triangle

25)

The sides are m + 11, 8m and m² + 1

m = 3

The sides are; 14, 24 and 10

Applying Pythagoras’s rule here

24 = √(14² + 10²)

24 ≠ 17.2

The sides does not represent a right angle triangle

28) the two sides are 9.2cm and 3.8cm

The range of values for the third sides will be

9.2 = √x² + 3.8²

x = √9.2² – 3.8²

x = 8.4

x = √9.2² + 3.8²

x = 10

The range of values for the third side is 8.4 ≤ x ≤ 10

Learn more on Pythagoras’s theorem here;

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