Question

DEF is an equilateral triangle where DM perpendicular to EF. Find the value of DM^2​

Answer 1

Given :-

• DEF is an equilateral triangle .
• DM ⟂ EF .

To Find :-

• DM² = ?

Solution :-

Let us assume that, each side of equaliteral ∆ is 'a' .

we know that,

• Perpendicular of an equaliteral ∆, bisects the base .

so,

→ EM = MF = (a/2) .

then, in Right angled ∆DME, we have,

→ DM² = DE² - EM² (By pythagoras theorem)

→ DM² = (a)² - (a/2)²

→ DM² = a² - (a²/4)

→ DM² = (4a² - a²)/4

→ DM² = (3a²/4) (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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Answer 2

Answer:

The value of DM² is :-

3a²/4