Question

triangle ABC is an isosceles triangle with ab is equal to AC the perimeter of the triangle is 36 cm and ab is equal to 10 cm find the area of the triangle ABC also find the length of altitude ad drawn on BC​

Answer 1

Answer:

length of BC = 16 cm

Ar. of triangle ABC = 48 cm^2

Step-by-step explanation:

we all know that isosceles triangle two sides are equal

so, sides of a triangle are:

a = 10 cm , b = 10 cm , c = ? ,

perimeter = 36 cm

peri. = a + b + c

36 = 10 + 10 + c

c = 16 cm

semi perimeter = a + b + c / 2

semi perimeter = 10 + 10 + 16 / 2

semi perimeter = 18 cm

Answer 2

Question :

Triangle ABC is an isosceles triangle with AB equal to AC. The perimeter of the triangle is 36 cm and AB is equal to 10 cm. Find the area of the triangle ABC also find the length of altitude AD drawn on BC.

Answer :

The area of the triangle ABC is 6 cm^2 and the length of altitude is 48 cm.

Given :

ABC is an isosceles triangle with AB equal to AC.

The perimeter of the triangle = 36 cm

AB = 10 cm

To find :

Area of the triangle ABC

Length of altitude AD drawn on BC

Solution :

Perimeter of a triangle = sum of length of all three sides

=> 36 = 10 + 10 + BC ( Since it is an isosceles triangle )

=> 36 = 20 + BC

=> 36 - 20 = BC

=> BC = 16

BC is the base of the triangle

Altitude of an isosceles triangle = = √(a^2 − b^2/4) where a is the length of two equal sides and b is the length of the base

= √(10^2 - 16^2/4)

= √(100 - 256/4)

= √(100 - 64)

= √36

= 6

We also know that, the area of a triangle = 1/2 × base × height

= 1/2 × 16 × 6

= 8 × 6

= 48

Hence, the area of the triangle ABC is 6 cm^2 and the length of altitude is 48 cm.

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