Question

Find the values of x and y in the picture. Express answers in simplest radical form. (square root form)

Answer 1

Answers:

x = 8

y = 15*sqrt(2)

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Explanation:

This is a 45-45-90 triangle. The right triangle is isosceles.

This means the two legs 3x-9 and x+7 are the same length

3x-9 = x+7

3x-x = 7+9

2x = 16

x = 16/2

x = 8

If x = 8, then each leg is...

3x-9 = 3(8)-9 = 24-9 = 15

x+7 = 8+7 = 15

Each leg is 15 units long to help confirm we have the correct x value.

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The hypotenuse y is exactly sqrt(2) times that of the leg length.

Therefore, y = 15*sqrt(2) since earlier we found each leg is 15 units long.

15*sqrt(2) = 21.213 approximately