Question

If the area of an equilateral triangle is 25√3 cm^2 , then the perimeter of the triangle is Single Correct Objective 10 cm 20 cm 30 cm 40 cm

Answer 1

Answer:

30cm

hope it may help you.....

Answer 2

ANSWER:

PERIMETER = 30 cm

GIVEN:

AREA = 25√3 cm²

Three sides are equal.

TO FIND:

Perimeter = ?

FORMULAS:

AREA = 1/2 bh

PERIMETER = b+b+b (Since it is an equilateral triangle)

Tan(theta) = OPPOSITE SIDE/ADJACENT SIDE

EXPLANATION:

Tan(60°) = h/(b/2)

h = (√3)b/2

Substitute in area formula

25√3 = 1/2 × b × √3b/2

25×4 = b²

b = √(100)

b = 10 cm

Substitute b in perimeter formula:

PERIMETER = 10 + 10 + 10

PERIMETER = 30 cm

CONFIRMATION OF b:

From Pythagoras theorem

b² = h² + (b/2)²

h² = b² - b²/4

h² = (4b² - b²)/4

h = √3 × b/2

NOTE 1 : AS THE GIVEN TRIANGLE IS AN EQUILATERAL TRIANGLE ALL THE THREE ANGLES ARE EQUAL TO 60°.

NOTE 2 : DIAGRAM IN ATTACHMENT.