Question

Please tell me the answes to this 25 points!

Answer 1

x = 4 , y = 2
`√(5)`

Explanation:

using Pythagoras' identity in both right triangles

a² + b² = c² ( c is the hypotenuse and a, b the legs )

Consider the right triangle on the left

with a = x , b = 3 and c = 5 , then

x² + 3² = 5²

x² + 9 = 25 ( subtract 9 from both sides )

x² = 16 ( take the square root of both sides )

`√(x^2)` =
`√(16)` , then

x = 4

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Consider the right triangle on the right

with a = y , b = x = 4 and c = 6 , then

y² + 4² = 6²

y² + 16 = 36 ( subtract 16 from both sides )

y² = 20 ( take the square root of both sides )

`√(y^2)` =
`√(20)` =
`√(4(5))` =
`√(4)` ×
`√(5)` = 2
`√(5)` , so

y = 2
`√(5)`