Question

In the given figure, $\triangle AMB \sim \triangle CMD$; determine MD in terms of x, y and z.

Answer 1

Answer:

The length of MD in terms of x, y and z is  xz/y.

Step-by-step explanation:

Given:  

ΔAMB ~ ΔCMD

From the figure : AM = y , MB = x , CM = z  

MB/MD = AM/CM

[Corresponding sides of two similar triangles are proportional]

x/MD = y/z

xz = MD × y

MD = xz/y

The length of MD in terms of x,y,and z =  xz/y

Hence, the length of MD is  xz/y.

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Answer 2

$\huge\bf\underline\mathcal\purple {Solution}$

Given :

=> $\triangle AMB \sim \triangle CMD$

● MD = ? (in terms of x , y and z )

Solve :

It is given that $\triangle AMB \sim \triangle CMD$.

Then ,

$\frac{MB}{MD}= \frac{AM}{MC}$

[The corresponding sides of similar triangles are always proportional ]

=> $\frac{x}{MD}= \frac{y}{z}$

=> $\frac{1}{MD}= \frac{y}{xz}$

=> $MD = \frac{xz}{y}$

Hence , the value of MD in terms of x , y and z is $\frac{xz}{y}$.