Question

A square of area 81 square metre has the same perimeter as that of an equilateral triangle.find the length of each side of the triangle​

Answer 1

Answer:

 length of each side of the triangle​ = 12m

Step-by-step explanation:

given that :

area of a square is 81m²

we know that formula for area of square is (side)²

let S be side of given square

so from area of a square is 81m²

S² = 81 m²

S = $\sqrt{81m^2}$

S = $\sqrt{(9)(9)(m)(m)}$

S = 9m

side of given square is 9m

also given that :

square has the same perimeter as that of an equilateral triangle

perimeter of square = perimeter of equilateral triangle

perimeter of square = 4(S)

perimeter of equilateral triangle = 3(a)

where a = side length of triangle

equilateral triangle has three sides equal. and square has its 4 sides equal

therefore; 4(S) = 3(a)

substitute value of S in above equation;

4(9)m = 3(a)

36m = 3a

a= (36)/3

a= 12m

 length of each side of the triangle​ =a = 12m