Question

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

Answer 1

Answer : 162 cm

Explanation:

Let us assume the equal sides to be x.

Given that base=80 cm.

 

=> Height of the isosceles triangle=\sqrt{x^{2}-40^{2}}x2−402 (using pythagoras theorem)

So, area=\frac{1}{2}bh21bh

360= \frac{1}{2}*80* < span > \sqrt{x^{2}-40^{2}} 21∗80∗<span>x2−402  

9=\sqrt{x^{2}-40^{2}}x2−402

81={x^{2}-40^{2}}x2−402

x^{2}=1681

x=41cm

=> Perimeter=41+41+80=162cm.

Cheers!

Answer 2

Answer :

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

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.