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Find the value of x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth.

Find the value of x. Assume that segments that appear to be tangent are tangent. Round-example-1
User Giulio Biagini
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1 Answer

8 votes
8 votes

Check the picture below.


\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{24+x}\\ a=\stackrel{adjacent}{24}\\ b=\stackrel{opposite}{32}\\ \end{cases}\implies (24+x)^2~~ = ~~24^2+32^2 \\\\\\ (24+x)(24+x)~~ = ~~24^2+32^2\implies \stackrel{F~O~I~L}{24^2+48x+x^2}~~ = ~~24^2+32^2 \\\\\\ 48x+x^2=32^2\implies x^2+48x-32^2=0\implies x^2+48x-1024=0 \\\\\\ (x-16)(x+64)=0\implies x= \begin{cases} 16~~\textit{\Large \checkmark}\\\\ -64 \end{cases}

notice, we didn't use -64, since the value of "x" must be a positive value.

Find the value of x. Assume that segments that appear to be tangent are tangent. Round-example-1
User Anil Maharjan
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3.1k points