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Question Number 82277 by M±th+et£s last updated on 19/Feb/20

Commented by M±th+et£s last updated on 19/Feb/20

find the area of  the rectangle

$${find}\:{the}\:{area}\:{of}\:\:{the}\:{rectangle} \\ $$

Commented by mr W last updated on 20/Feb/20

is the triangle equilateral?

$${is}\:{the}\:{triangle}\:{equilateral}? \\ $$

Commented by M±th+et£s last updated on 20/Feb/20

no its isosceles triangle

$${no}\:{its}\:{isosceles}\:{triangle}\: \\ $$

Commented by mr W last updated on 20/Feb/20

then no unique solution!    area of rectangle=a×b  but we have only  (√(((a/6))^2 +b^2 ))=(√5)  (a^2 /(36))+b^2 =5

$${then}\:{no}\:{unique}\:{solution}! \\ $$$$ \\ $$$${area}\:{of}\:{rectangle}={a}×{b} \\ $$$${but}\:{we}\:{have}\:{only} \\ $$$$\sqrt{\left(\frac{{a}}{\mathrm{6}}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} }=\sqrt{\mathrm{5}} \\ $$$$\frac{{a}^{\mathrm{2}} }{\mathrm{36}}+{b}^{\mathrm{2}} =\mathrm{5} \\ $$

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