Question

In triangle ABC is an equilateral triangle.D,E are the mid points of AB and AC respectively.If DE is equal to 3cm,then the perimeter of triangle ABC is​

Answer 1

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Secondary SchoolMath 5 points

Triangle ABC is an equilateral triangle . D and E are mid points of side BC and AB respectively . If BC =4cm , find area of triangle BED.

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Answers

Rampranav

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Here D and E are mid points of BC and AB , We join DE and from " converse of mid-point theorem " we get AC | | ED

And BC = 4 cm , SO

AB = BC = CA = 4 cm ( As given ABC is a equilateral triangle )

And

D and E are mid points of BC and AB , So

BE = EA = BD = DC = 2 cm

Now In ∆ BAC and ∆ BED

∠ ABC = ∠ EBD ( Same angles )

∠ BAC = ∠ BED ( As we know AC | | ED and take AB as transversal line , So these angles are Corresponding angles )

And

∠ BCA = ∠ BDE ( As we know AC | | ED and take CB as transversal line , So these angles are Corresponding angles )

Hence ∆ BAC ~ ∆ BED ( By AAA rule )

So we know

BA÷BE = AC÷ED⇒4÷2 = 4÷ED⇒ED = 2

And

Area of BAC÷Area of BED = AC²÷ED²⇒Area of BAC÷Area of BED = 4²÷2²⇒Area of BAC÷Area of BED = 16÷4

So,

Area of ∆ BED = 4 cm2 ( Ans )