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Assume that the wooden triangle shown is a right triangle.
​​ a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram. Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.

Assume that the wooden triangle shown is a right triangle a Write an equation using the Pythagorean Theorem and the measurements provided in the diagram Hint l class=

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Answer:

Part 1) [tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) The answer in the procedure

Step-by-step explanation:

Part 1)

we know that

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

we have

[tex]c=(10x+15y)[/tex]

[tex]a=(6x+9y)[/tex]

[tex]b=(8x+12y)[/tex]

substitute the values

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) Transform each side of the equation to determine if it is an identity

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}\\ \\100x^{2}+150xy+225y^{2}=36x^{2}+54xy+81y^{2}+64x^{2}+96xy+144y^{2}\\ \\100x^{2}+150xy+225y^{2}=100x^{2}+150xy+225y^{2}[/tex]

The left side is equal to the right side

therefore

Is an identity

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Answer:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

Step-by-step explanation:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.

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