Question

The equal sides of the isocceles triangle are 12 cm and the perimeter is 30 cm the area of this triangle is

Answer 1

Answer:

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Step-by-step explanation:

Length of the equal sides = 12cm

Perimeter of the triangle = 30cm

Length of the third side = 30 - (12+12) cm = 6cm

Semi perimeter of the triangle(s) = 30/2 cm = 15cm

Using heron's formula,

Area of the triangle = √s (s-a) (s-b) (s-c)

                                      = √15(15 - 12) (15 - 12) (15 - 6)cm2

                                      = √15 × 3 × 3 × 9 cm2

                                      = 9√15 cm2

Answer 2

$\bigstar \large \sf \underline{\underline{Given:-}}$

• The equal sides of the isocceles triangle are 12 cm.
• The perimeter is 30 cm.

$\bigstar \sf \large \underline{\underline{To \ Find :- }}$

• The area of this triangle.

$\bigstar \sf \large \underline{\underline{Solution:-}}$

Let 'x' be the third side .

We know :

❥ Perimeter = sum of all sides.

Acc to question :

➜ Perimeter = 12 + 12 + x

=> 30 = 24 + x

=> x = 30 - 24

=> x = 6

Therefore, third side is 6cm.

The Area of triangle ;-

We Know :

Heron's formula :-

$\bigstar \boxed{\orange{\sf Area \ of \ triangle =\sqrt{s(s-a)(s-b)(s-c)} }}$

Where,

➜ s = a+b+c / 2 & a;b;c are sides of triangle.

➜ S = 30 / 2 = 15cm.

Now ,

$\implies \sf Area \ of \ triangle = \sqrt{15(15-12)(15-12)(15-6)} \\\\\implies \sf \sqrt{15(3)(3)(9)} cm^2 \\\\\implies \sf 9\sqrt{15} cm^2.$

Therefore ,

❥ Area of triangle is 9√15 cm².

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HOPE IT HELPS !