# For a $\vartriangle {\text{XYZ}}$, ${\text{ZY}} = 12{\text{ m}}$, ${\text{YX}} = 8{\text{ m}}$ and ${\text{XZ}} = 10{\text{ m}}$. If $\vartriangle {\text{ZYX}} \cong \vartriangle {\text{ABC}}$, then the length of side AC (in meters) is

$

{\text{A}}{\text{. 10}} \\

{\text{B}}{\text{. 12}} \\

{\text{C}}{\text{. 8}} \\

{\text{D}}{\text{. 1}} \\

$

Last updated date: 18th Mar 2023

•

Total views: 308.4k

•

Views today: 7.88k

Answer

Verified

308.4k+ views

Hint- Here, we will be using the property that the length of the corresponding sides will be equal in any two congruent triangles.

Given, in a $\vartriangle {\text{XYZ}}$, ${\text{ZY}} = 12{\text{ m}}$, ${\text{YX}} = 8{\text{ m}}$ and ${\text{XZ}} = 10{\text{ m}}$

Since we know that for any two congruent triangles, the corresponding sides are always equal.

Also given that $\vartriangle {\text{ZYX}} \cong \vartriangle {\text{ABC}}$

Clearly from the figure, we can see that the side AB in $\vartriangle {\text{ABC}}$ is corresponding to side XY in $\vartriangle {\text{XYZ}}$, side BC in $\vartriangle {\text{ABC}}$ is corresponding to side YZ in $\vartriangle {\text{XYZ}}$ and side AC in $\vartriangle {\text{ABC}}$ is corresponding to side XZ in $\vartriangle {\text{XYZ}}$.

i.e., we can say ${\text{AB}} = {\text{XY}} = {\text{YX}} = 8{\text{ m}}$, ${\text{BC}} = {\text{YZ}} = {\text{ZY}} = 12{\text{ m}}$ and ${\text{AC}} = {\text{XZ}} = 10{\text{ m}}$.

Hence, the length of side AC is 10 meters.

Therefore, option A is correct.

Note- In these type of problems, the corresponding sides of the given congruent triangles are needed to be identified carefully with the help of their diagrams.

Given, in a $\vartriangle {\text{XYZ}}$, ${\text{ZY}} = 12{\text{ m}}$, ${\text{YX}} = 8{\text{ m}}$ and ${\text{XZ}} = 10{\text{ m}}$

Since we know that for any two congruent triangles, the corresponding sides are always equal.

Also given that $\vartriangle {\text{ZYX}} \cong \vartriangle {\text{ABC}}$

Clearly from the figure, we can see that the side AB in $\vartriangle {\text{ABC}}$ is corresponding to side XY in $\vartriangle {\text{XYZ}}$, side BC in $\vartriangle {\text{ABC}}$ is corresponding to side YZ in $\vartriangle {\text{XYZ}}$ and side AC in $\vartriangle {\text{ABC}}$ is corresponding to side XZ in $\vartriangle {\text{XYZ}}$.

i.e., we can say ${\text{AB}} = {\text{XY}} = {\text{YX}} = 8{\text{ m}}$, ${\text{BC}} = {\text{YZ}} = {\text{ZY}} = 12{\text{ m}}$ and ${\text{AC}} = {\text{XZ}} = 10{\text{ m}}$.

Hence, the length of side AC is 10 meters.

Therefore, option A is correct.

Note- In these type of problems, the corresponding sides of the given congruent triangles are needed to be identified carefully with the help of their diagrams.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write the 6 fundamental rights of India and explain in detail

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Name the 8 union territories of India

What are merits and demerits of democracy

Define human made resources

What is pollution? How many types of pollution? Define it

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.