Question

In an equilateral triangle PQR seg PS is perpendicular to side BC then PS^=?​

Answer 1

Step-by-step explanation:

hope it helps u

the ans in image with explanation

Answer 2

Concept

Pythagoras theorem says that in a right angled triangle the square of hypotenuse is equal to the addition of square of base and perpendicular.

$H^{2} =P^{2} +B^{2}$

Given

Triangle PQR is an equilateral triangle.

To find

Length of PS if Triangle PQR is an equilateral triangle. and PS is perpendicular to side QR.

Explanation

let the length of equilateral triangle is x.

PS is perpendicular on QR such that QS=x/2

In triangle PQS

$PS^{2}=PQ^{2} -QS^{2}$

$PS^{2}$=$x^{2} -x/2^{2}$

PS=$\sqrt{x^{2} -x^{2} /4}$

=$\sqrt{3x^{2} /4}$

x is the square root of $x^{2}$ and 2 is the square root of 4.

=$\sqrt{3}x/2$

If we apply in another triangle then we get the same answer.

Hence the length of PS=$\sqrt{3}/2* side of equilateral triangle$ if PQR is an equilateral triangle.

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