Question

ABC and BDE are two equilateral triangles such that D is the midpoint of BC.Ratio of the areas of triangles ABC and BDE is

A
2:1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1:2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4:1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
1:4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 4:1Given:△ABC and △BDE are equilateral.BD=12BC as D is the midpoint of BCSince △ABC and △BDE are equilateral.Their sides would be in the same ratioABBE=ACED=BCBDHence by SSS similarity,△ABC∼△BDEAnd, we know that the ratio of area of triangle is equal to the ratio of the square of corresponding sides.So,areaof△ABCareaof△BDE=BC2BD2=BC2(BC2)2 since BD=BC2=4BC2BC2=41Hence areaof△ABCareaof△BDE=41=4:1

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Congruent Triangles
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program