Question

- A square and an equilateral triangle have the same perimeter. If
the diagonal of the square is 12√5 cm, then find the altitude of
equilateral triangle ​

Answer 1

diagonal of sq = a√2

12√5 = a√2

12√5/√2=a

a= 12√5×√2/√2×√2

a = 12√10/2

a = 6√10

perimeter of sq = 4a

= 4×6√10

=24√10 = perimeter of equi∆

3a= 24√10

a=8√10

i.e side of equi∆

we know that -

area of equi ∆ =√3/4 into side^2 =1/2 base × height

√3/4 × (8√10)^2=1/2 × 8√10 × height

√3/4×64×10 =4√10× height

160√10= 4√10× height

on solving

height = 40cm

Answer 2

therefore, the altitude of the equilateral triangle is 4√30.