इफ एबीसी इज एन लेटरल ट्रायंगल व्हिच ऑफ द एंगल इज इक्वल टू
Answers
Step-by-step explanation:
7th
Maths
The Triangle and Its Properties
Isosceles and Equilateral Triangles
ABC is an isosceles triangl...
MATHS
avatar
Asked on December 27, 2019 by
Charishma Punitha
ABC is an isosceles triangle right angled at B. Equilateral ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ΔABE and ΔACD .
MEDIUM
Share
Study later
ANSWER
Given that:- △ABC is an isosceles triangle and ∠ABC=90°
∴AB=BC
△ABE∼△ACD(∵All equilateral triangles are similar)
To find:-
ar(△ACD)
ar(△ABE)
=?
Solution:-
In △ABC,
Using pythagoras theorem,
AC
2
=AB
2
+BC
2
AC
2
=AB
2
+AB
2
[∵AB=AC]
AC
2
=2AB
2
.....(i)
Now In △ABE and △ACD
△ABE∼△ACD(Given),
As we know that ratio of area of similar triangles is equal to the ratio of squares of their corresponding sides.
∴
ar(△ACD)
ar(△ABE)
=
AC
2
AB
2
⇒
ar(△ACD)
ar(△ABE)
=
2AB
2
AB
2
[From(i)]
⇒
ar(△ACD)
ar(△ABE)
=
2
1
⇒ar(△ABE):ar(△ACD)=1:2
Hence the ratio between the area of △ABE to the area of △ACD is 1:2.
Answer:
the three angles of the equilateral triangle are congruent and equal to 60 degrees. Suppose, ABC is an equilateral triangle, then, as per the definition; AB = BC = AC, where AB, BC and AC are the sides of the equilateral triangle.