234k views
13 votes
Hello help me with this question thanks in advance​

Hello help me with this question thanks in advance​-example-1

1 Answer

6 votes


\bold{\huge{\underline{ Solution \:1}}}

  • Yes, ΔEDF and ΔBCA are similar

If we look at the both the triangles then the


  • \sf{ {\angle} E = {\angle}B }

  • \sf{ {\angle} F = {\angle}A }

From above, we can conclude that :-

Both the triangles are similar by AA Similarity

Hence, Option A is correct.


\bold{\huge{\underline{ Solution \:2}}}

Let consider the given triangle be ABC and the line that divides the triangle consider it as DE

  • Here, DE || BC

So,


  • \sf{( AD )/( AB )}{\sf{ = }}{\sf{(AE)/(AC)}}{\sf{=}}{\sf{(DE)/(BC)}}

Therefore,

  • ΔABC similar to ΔADE by SSS congruence similarity criterion.

Now,

We have to find the value of x

In ΔABC, By using BPT theorem

  • If the line is drawn parallel to one side of the triangle which intersect the other two sides at specific points then the other two sides are in proportion .

That is,


\sf{( AD )/( AB )}{\sf{ = }}{\sf{(DE)/(BC)}}

Subsitute the required values,


\sf{( 6 )/( 6 + 4 )}{\sf{ = }}{\sf{(8)/(x)}}


\sf{( 6 )/( 10 )}{\sf{ = }}{\sf{(8)/(x)}}


\sf{( 3 )/( 5 )}{\sf{ = }}{\sf{(8)/(x)}}


{\sf{ x = 8{*} }}{\sf{(5)/(3)}}


{\sf{ x = }}{\sf{(40)/(3)}}


{\sf{ x = 13}}{\sf{(1)/(3)}}

Hence, Option C is correct


\bold{\huge{\underline{ Solution \:3}}}

Here,

  • SRT similar to BAC

For x,

By using BPT theorem,


\sf{( AB )/( RS )}{\sf{ = }}{\sf{(BC)/(ST)}}

Subsitute the required values,


\sf{( 2 )/( 4 )}{\sf{ = }}{\sf{(x)/(6)}}


\sf{( 1 )/( 2 )}{\sf{ = }}{\sf{(x)/(6)}}


\sf{ x = }{\sf{(6)/(2)}}


\sf{ x = 3 }

Thus, The value of x is 3

For y

Again by using BPT theorem,


\sf{( AB )/( RS )}{\sf{ = }}{\sf{(AC)/(RT)}}

Subsitute the required values,


\sf{( 2 )/( 4 )}{\sf{ = }}{\sf{(5)/(y)}}


\sf{( 1 )/( 2 )}{\sf{ = }}{\sf{(5)/(y)}}


\sf{ y = 5{*}2 }


\sf{ y = 10 }

Thus, The value of y is 10

Hence, Option A is correct.

User Amaranth
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories