Question

If it is an isosceles triangle, can the third side be of length 13 cm? Justify your
answer.

Answer 1

Step-by-step explanation:

Solution

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Area of thee triangle =

s(s−a)(s−b)(s−c)

s=

2

a+b+c

=

2

13+13+10

=

2

36

=18cm

Area of the triangle =

18(18−13)(18−13)(18−10)

=

2×3×3×5×5×2×2×2

=60sq.cm

Answer 2

Answer:

Therefore, area of the triangle is 60.

Step-by-step explanation:

We know that the length of two sides in isosceles triangle is equal. Given that one of the equal lineis of 13 cm, so length of other side should also be 13 cm.

Now,

Length of equal to sides = 13 cm each

Perimeter of triangle = 50 cm

→ Perimeter of triangle = sum of equal

sides + base side (3rd side)

Rightarrow50 cm=13 cm+13 cm+3rd si

- 50 cm = 26 cm + 3rdside

Rightarrow50 cm-26 cm=3rd side

24 cm=3rd side

Length of third side is 24 cm.

Then,

Semi perimeter of the triangle =1/2x perimeter of the triangle

Semi perimeter of the triangle =1/2x

50 cm

Semi perimeter of the triangle = 25 cm

By Heron's formula

Area = sqrt((s - a)(s - b) * (s - c)

therefore, applying heron's formula for the area of the triangle.

Rightarrow Area= sqrt 25(25-13)(25-13)(25-

Rightarrow Area= sqrt 25*12*12*1cr

Rightarrow Area= sqrt 5^ 2 *12^ 2

Rightarrow Area=5*12cm^ 2

=Area=60cm^ 2

cm^ ^ 2

Therefore, area of the triangle is 60