Question

I need serious help with this one. Dont mind the answer choice I clicked I was choosing things

Answer 1

The expression which is not equivalent to (PQ)² + (QR)² is c²(x + y).

Explanation:

From inspection of the given triangle:

`PQ = a \implies (PQ)^2 = a^2`

`QR = b \implies (QR)^2 = b^2`

Therefore:

`(PQ)^2 + (QR)^2 = a^2 + b^2`

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Given:

`(PQ)/(PR)=(PS)/(PQ) \implies (a)/(c)=(x)/(a)\implies a^2=cx`

`(PR)/(QR)=(QR)/(RS) \implies (c)/(b)=(b)/(y)\implies b^2=cy`

Therefore:

`\begin{aligned}a^2 + b^2&=cx+cy\\\implies (PQ)^2 + (QR)^2 &= cx+cy\end{aligned}`

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According to Pythagoras Theorem:

`a^2+b^2=c^2`

Therefore:

`\begin{aligned}a^2 + b^2&=c^2\\\implies (PQ)^2 + (QR)^2 &= c^2\\ \implies (PQ)^2 + (QR)^2 &= (c)(c)\end{aligned}`

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Therefore, the expression which is not equivalent to (PQ)² + (QR)² is:

• c²(x + y)