Question

the base of an isocelous triangle is 6 cm and each of its side is 5 cm find the hieght of the triangle​ by herons formula

Answer 1

Step-by-step explanation:

By herons formula

s=6+5+5/2

=16/2

s=8

Area of triangle=root[s(s-6)(s-5)(s-5)]

=root[8(8-2)(8-5)(8-5)]

=root(8×2×3×3]

=2×2×3

=12 cm^2

Area of triangle is 12cm^2.

Also area of triangle=1/2×h×b

12=1/2×h×6

12=h×3

h=12/3

h= 4 cm

The height of triangle is 4cm

Answer 2

Step-by-step explanation:

Given -

Base of an isosceles triangle is 6 cm

Each of its side is 5 cm

To Find -

Height of the isocelses triangle

As we know that,

• In isocelses triangle two sides are equal.

Heron's formula = √s(s-a)(s-b)(s-c)

here,

s = semiperimeter = a+b+c/2

a = side

b = side

c = side

Now,

s = 6+5+5/2 = 16/2 = 8

Then,

Area = √s(s-a)(s-b)(s-c)

= √8(8-6)(8-5)(8-5)

= √8×2×3×3

= √144

• = 12 cm²

Now,

Height = 1/2√4a²-b²

here,

a = side (two similar side)

b = base

= 1/2√4(5)²-(6)²

= 1/2√4×25-36

= 1/2√100-36

= 1/2√64

= 1/2 × 8

= 4 cm

Hence,

The height of the isocelses triangle is 4 cm.

Formula Used -

Heron's formula = √s(s-a)(s-b)(s-c)

For height of isocelses triangle =

1/2√4a²-b²