Question

The given figure shows an equilateral triangle ABC with each side 15 cm. Also DE||BC, DF||AC and EG||AB. If DE + DF + EG = 20 cm, find FG.

• A. 5 cm.
• B. 10 cm
• C. 2.5 cm
• D. 7.5 cm

Answer 1

The correct option is A 5 cm.

Given, $△ABC$ is an equilateral triangle.$DE\parallel BC$, $DF\parallel AC$
$EG\parallel AB$
In $△ADE$ and $△ABC$
$\angle ADE=\angle ABC=60$ (Corresponding angles)
$\angle AED=\angle ACB=60$ (Corresponding angles)
Thus, $△ADE$ is an equilateral triangle.
Similarly, $△DBF$ and $△EGC$ are equilateral triangle.
In $△DBF$ and $△EGC$
$\angle DBF=\angle ECG$
$\angle BDF=\angle GEC$
$BD=EC$ (since, $AB=AC$ and $AD=AE$, Thus, $AB-AD=AC-AE$)
Thus, $△DBF\cong △EGC$ (ASA rule)
or, $BF=GC$ (CPCT)
Therefore, $DE+DF=AD+DB=AB=15$
and, $DE+DF+EG=20$
Thus, $EG=5$ cm
Hence, $EG=GC=BF=5$
or $BC=15$
$BF+FG+GC=15$
$FG=5$ cm