Question

The length of equal sides of an isosceles triangle is 12 units each and the perimeter is 30 units. What is the area of the triangle?
1 216√5 sq units
2 1215 sq units
3 27√5 sq units
4 9√15 sq units

Answer 1

Perimeter of isosceles triangle=30cm

Length of equal sides=12cm

Let third side of triangle=xcm

According to problem,

x+12+12=30

x+24=30

x=30−24

x=6

∴ Third side of triangle=6cm

Using Heron's formula

Area of triangle=

s(s−a)(s−b)(s−c)

sq. units

where s=

2

a+b+c

s=

2

30

=15

Area of triangle=

15(15−12)(15−12)(15−6)

cm

2

=

15×3×3×9

cm

2

=3×3×

15

cm

2

=9

15

cm

2

∴ Area of triangle=9

15

cm

2

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Answer 2

Answer:

4. 9√15 units

Step-by-step explanation:

Question says that, an isoceles triangle with two equal sides measures 12 units each. perimeter is 30 units. find the area.

Step 1 : Find the third side of the isosceles triangle :

Perimeter of a triangle : Sum of all sides

→ 12 + 12 + third side = 30 units

→ 24 + third side = 30 units.

→ third side = 30 - 24 units

→ third side = 6 units.

Step 2 : Find the area of the triangle :

[Using the heron's formula ]

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

Where,

• s (semi-perimeter) = 15 units.
• 'a', 'b', and 'c' are the three sides of the triangle.

So, area of the triangle is :

→ √15(15 - 12)(15 - 12)(15 - 6)

→ √15(3)(3)(9)

→ √15 × 3 × 3 × 3 × 3

→ √15 × 3² × 3²

→ 3 × 3√15

→ 9√15 units.

The area of the triangle is 9√15 units.