Question

Assume that the wooden triangle shown is a right triangle.

Answer 1

Answer:

Part 1) $(10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}$

Part 2) The answer in the procedure

Step-by-step explanation:

Part 1)

we know that

Applying the Pythagoras Theorem

$c^{2}=a^{2}+b^{2}$

we have

$c=(10x+15y)$

$a=(6x+9y)$

$b=(8x+12y)$

substitute the values

$(10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}$

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

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

The left side is equal to the right side

therefore

Is an identity

Answer 2

Answer:

b. $\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2$

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

Step-by-step explanation:

b. $\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2$

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

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

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