Question

The area of an isosceles triangle EFG is 60m2 and EF=EG=13m.find the measure of FG.

• A. undefined
• B. undefined
• C. undefined
• D. undefined

Answer 1

Area of Isosceles triangle = $\frac{1}{2}\times FG\left(base\right)\times EX\left(height\right)=60m^2$
$\to {60}^2=\frac{1}{4}\times F{G}^2\times E{X}^2$ ....(1)
$E{X}^2=E{G}^2-{\left(\frac{FG}{2}\right)}^2={13}^2-\frac{F{G}^2}{4}$
Substituting ln (i), we get,
$3600=\frac{1}{4}\times F{G}^2\times (169-\frac{F{G}^2}{4})$
$=\frac{1}{16}(169\times 4F{G}^2-F{G}^4)$
$\to F{G}^4-676F{G}^2+57600=0$
solving, $F{G}^2=676\pm \frac{476}{2}=576or100M$
$FG=24Mor10M$