Geometry (1 Viewer)

Green Yoda · Nov 13, 2015

help with b.

InteGrand · Nov 13, 2015

Rathin said:
View attachment 32673
help with b.

$We should write $\triangle CLW$ is similar to $\triangle TLE$ so that the corresponding sides match up as written (i.e. $CL$ corresponds to $TL$, etc.), rather than the way the question wrote it in part (a).$

$Now, let $TL=x$. Then$

$\begin{align*}\frac{WL}{LC}&= \frac{EL}{LT} \quad (\text{corresponding sides in similar triangles }CLW \text{ and }LTE\text{ are in equal ratio}) \\ \Rightarrow \frac{5+x}{21}&=\frac{6}{x} \\ \Rightarrow x^2 + 5x &= 21\times 6\\ \Rightarrow x ^2 + 5x - 126 &= 0 \\ \Rightarrow x &= \frac{-5\pm \sqrt{5^2 +4 \times 126}}{2}\\ &=\frac{-5\pm 23}{2}\\ &= \frac{-5+ 23}{2} \quad (\text{taking just the positive solution since }x>0) \\ &=9.\end{align*}$

$Therefore, $TL$ has length 9 cm.$

Green Yoda · Nov 13, 2015

InteGrand said:
$We should write $\triangle CLW$ is similar to $\triangle TLE$ so that the corresponding sides match up as written (i.e. $CL$ corresponds to $TL$, etc.), rather than the way the question wrote it in part (a).$

$Now, let $TL=x$. Then$

$\begin{align*}\frac{WL}{LC}&= \frac{EL}{LT} \quad (\text{corresponding sides in similar triangles }CLW \text{ and }LTE\text{ are in equal ratio}) \\ \Rightarrow \frac{5+x}{21}&=\frac{6}{x} \\ \Rightarrow x^2 + 5x &= 21\times 6\\ \Rightarrow x ^2 + 5x - 126 &= 0 \\ \Rightarrow x &= \frac{-5\pm \sqrt{5^2 +4 \times 126}}{2}\\ &=\frac{-5\pm 23}{2}\\ &= \frac{-5+ 23}{2} \quad (\text{taking just the positive solution since }x>0) \\ &=9.\end{align*}$

$Therefore, $TL$ has length 9 cm.$

omg stupid textbook...I thought they are suppose to put it in order. Also i assume the answer of the textbook is also wrong..it says 2.

InteGrand · Nov 13, 2015

Rathin said:
omg stupid textbook...I thought they are suppose to put it in order. Also i assume the answer of the textbook is also wrong..it says 2.

$Yeah it can't be 2 since $TL$ is the hypotenuse of triangle $TLE$, so $TL>EL\Rightarrow TL > 6$. And usually in the HSC exams, they do put the vertices of the similar triangles in the right order. But you should just quickly check to make sure that they are indeed in the right order first.$

$To check it, you can mark in the angles that are equal. Like, the right angles are drawn, and you can put an angle ``arc'' symbol in the places of angles $LTE$ and $LCW$, and a dot in the places of angle $L$. This shows us which angles in the triangles are equal, and then the vertices that correspond to each other in the triangles are the ones with equal angle, so $L$ corresponds to $L$, $T$ corresponds to $C$ and $E$ corresponds to $W$.$

axwe7 · Dec 13, 2015

Lol, NCM.... XD

Geometry (1 Viewer)

Green Yoda

Hi Φ

InteGrand

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Green Yoda

Hi Φ

InteGrand

Well-Known Member

axwe7

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