Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
Share
Notifications

View all notifications

Find the Length of the Side and Perimeter of an Equilateral Triangle Whose Height is √ 3 Cm. - Geometry

Login
Create free account


      Forgot password?

Question

Find the length of the side and perimeter of an equilateral triangle whose height is \[\sqrt{3}\] cm.

 

Solution

Since, ABC is an equilateral triangle, CD is the perpendicular bisector of AB.
Now, According to Pythagoras theorem,
In ∆ACD

\[{AC}^2 = {AD}^2 + {CD}^2 \]
\[ \Rightarrow \left( 2a \right)^2 = a^2 + \left( \sqrt{3} \right)^2 \]
\[ \Rightarrow 4 a^2 - a^2 = 3\]
\[ \Rightarrow 3 a^2 = 3\]
\[ \Rightarrow a^2 = 1\]
\[ \Rightarrow a = 1 cm\]

Hence, the length of the side of an equilateral triangle is 2 cm.
Now,
Perimeter of the triangle = (2 + 2 + 2) cm
                                        = 6 cm
Hence, perimeter of an equilateral triangle is 6 cm.

  Is there an error in this question or solution?

APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 2: Pythagoras Theorem
Problem Set 2 | Q: 5 | Page no. 44
Solution Find the Length of the Side and Perimeter of an Equilateral Triangle Whose Height is √ 3 Cm. Concept: Similarity in Right Angled Triangles.
S
View in app×