Question

for an equilateral triangle find 1) area when its perimeter is 48cm. 2) perimeter when its area is 144√3 cm

Answer 1

THERE R TWO FORMULAS TO BE USED
1) @@PERIMETER OF EQUILATERAL TRIANGLE = 3 × SIDES
2) @@ AREA OF EQUILATERAL TRIANGLE = ( ROOT 3 / 4 )× SIDES^2

SO UR ANS IS ( A = SIDES )

1) => PERIMETER = 3 × A
=> 48 = 3 × A
=> 48/3 = A
=> 16 = A
=> AREA = ( ROOT 3 / 4 ) A^2
= ( ROOT 3 / 4) 16 × 16
= ROOT 3 × 4 × 16
= 64 ROOT 3

2) => AREA = ROOT 3 / 4 × A^2
=> A^2 = (144 × root 3 × 4 ) / root 3
=> A^2 = 144 × 4
=> A^2 = 576
=> A = 24

=> PERIMETER = 3 × A
= 24


SO FINALLY UR ANSWER IS

1) => AREA = 64 ROOT 3

2) => PERIMETER = 24

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