Question

the base of an isosceles triangle measures 80 cm and its area is 360 square cm find the perimeter of the triangle

Answer 1

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Answer 2

Answer :

• The Perimeter of the isosceles triangle , p = 161 cm.

Explanation :

Explanation :Given :

• Base of the isosceles triangle, S = 80 cm

• Area of the isosceles triangle, A = 360 cm²

To find :

• Perimeter of the isosceles triangle , P = ?

Solution :

• First let us find the equal side of the isosceles triangle.

• We know the formula for area of a isosceles triangle i.e,

⠀⠀⠀⠀⠀⠀⠀⠀A = b/4√(4a² - b)

Where :

• A = Area of the isosceles triangle
• a = Equal side of the triangle
• b = Base of the triangle

Now by using the formula for area of a isosceles triangle and substituting the values in it, we get :

→ A = b/4√(4a² - b²)

→ 360 = 80/4 × √(4a² - 80²)

→ 360 = 20 × √(4a² - 6400)

→ 360/20 = √(4a² - 6400)

→ 18 = √(4a² - 6400)

→ 18² = 4a² - 6400

→ 324 = 4a² - 6400

→ 324 + 6400 = 4a²

→ 6724 = 4a²

→ 6724/4 = a²

→ 1681 = a²

→ √1681 = a

→ 41 = a

∴ a = 41 cm

Hence the equal side of the isosceles triangle is 41 cm .

Now to find the perimeter of the triangle :

We know the formula for perimeter of a triangle i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀Perimeter = Sum of all sides

Now using the above formula and substituting the values in it, we get :

→ P = sum of all sides

→ P = 41 + 41 + 80 [Since the two equal sides are there , a = 41 ]

→ P = 162

∴ P = 162 cm

Therefore,

Perimeter of the triangle is 162 cm.