Question

Help in solving geometry

Answer 1

Therefore

`x=15\\\\y=4`

Explanation:

Consider the Figure as shown below where

DE || BC

i.e ME || FC

AD = 12

AE = 18

MF = 5

EC = 6

To Find:

AM = x = ?

DB = y = ?

Solution:

We Know that

Basic Proportionality Theorem:

Basic Proportionality Theorem states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

In Δ AFC

ME || FC

`(AM)/(MF)=(AE)/(EC)`.....Basic Proportionality Theorem

substituting the values we get

`(x)/(5)=(18)/(6)\\\\\therefore x=3* 5=15`

Similarly,

In Δ AFC

ME || FC

`(AD)/(DB)=(AM)/(MF)`......Basic Proportionality Theorem

substituting the values we get

`(12)/(y)=(15)/(5)\\\\\therefore y=(12)/(3)=4`

Therefore

`x=15\\\\y=4`