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polet [3.4K]
3 years ago
7

Help ASAP: Find the length of RT

Mathematics
1 answer:
bixtya [17]3 years ago
8 0

Answer:

32

Step-by-step explanation:

the equation of a right triangle is x^2 + y^2 = z^2, where x and y are the legs and z is the hypotenuse

write the equations for triangles QTS and STR:

RT^2 + TS^2 = 40^2

7^2 + TS^2 = 25^2

then solve for RT:

RT^2 - 7^2 = 40^2 - 25^2 (subtract second equation from first)

RT^2 = 1024

RT = 32

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Answer:

The size of side x can range from 0.5 < x < 16.5.

The size of side x cannot take on values 0 and 16.5, but it ranges between those two values for side x to complete a triangle with those two other sides.

Step-by-step explanation:

Complete Question

What is the range of possible sizes for side x? One Side is 8.5 the other is 8.0.

Solution

With the logical assumption that the three sides are to form a triangle

Let the two sides given be y and z

And the angle between y and z be θ

The angle θ can take on values from 0° to 180° without reaching either values.

As θ approaches 0°, (x+z) becomes close to equaling y. (x + z) < y

It can never equal y, because θ can never be equal to 0°, if a triangle is to exist.

Hence, x > (z−y)

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As θ approaches 180°, x approaches the sum y+z, θ can never equal 180° if a triangle is to exist, so x never equals (y+z).

Hence x < (y+z)

x < 8 + 8.5

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Hope this Helps!!!

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