Question

The base of an isosceles triangle measures 24cm and its area is 60 cm^2. Find its perimeter (Using Heron's formula).

Answer 1

Answer:

$\huge\colorbox{blue}{P=50}$

Step-by-step explanation:

hope it help you

Answer 2

Step-by-step explanation:

Given :

Base of an isosceles triangle is 24 cm.

Area of isosceles triangle is 60 cm².

Find :

The perimeter of isosceles triangle.

Solution :

Let each equal side of isosceles triangle be a cm.

Then :

$s \: = \frac{a + a + 24}{2} \: cm$

$= > (a + 12) \: cm.$

By Heron's formula :

$the \: area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)}$

$= > \sqrt{(a + 12)(a + 12- a)(a + 12 - a)(a + 12 - 24)} = 60 \: \: (given)$

$= > \sqrt{(a + 12) \times 12 \times 12 \times (a - 12)} = 60$

$= > 12\sqrt{(a + 12)(a - 12)} = 60$

$= > \sqrt{ {a}^{2} - 144 } = 5$

$= > {a}^{2} - 144 = 25$

$= > {a}^{2} = 169$

$= > a = \sqrt{169}$

$= > a = 13.$

Hence :

The perimeter of isosceles triangle is = 13 cm + 13 cm + 24 cm = 50 cm.

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