Question

The sides of triangle are 8cm,11cm and 13cm.The altitude of the smallest side

Answer 1

Answer:

The sides of triangle are 8 cm, 11 cmand 13 cm.

Semi-perimeter =8+11+13/2

=16

Using heron's formula,

Area =

$\sqrt{16(16 - 8)(16 - 11)(16 - 13)}$

=

$\sqrt{16 \times 8 \times 5 \times 3}$

=

$\sqrt{8 \times 2 \times 8 \times 5 \times 3}$

=

$8 \sqrt{30}$

Altitude (h) =

$1 \div 2 \times 8 \times h = 8 \sqrt{30}$

$h = 2 \sqrt{30}$

Answer 2

The altitude of the smallest side is 2√30

Step-by-step explanation:

The sides of triangle are 8cm,11cm and 13cm.

using herons formula to calculate the area of the triangle

a = 8 cm

b = 11 cm

c = 13 cm

$s = \frac{a+b+c }{2}\\ s = \frac{8+11+13}{2}\\ s= \frac{32}{2}\\ s= 16$

area = $\sqrt{s(s-a)(s-b)(s-c)}$

$= \sqrt{16(16-8)(16-11)(16-13)}\\= \sqrt{16\times 8\times5\times3}\\ = \sqrt{2\times2\times2\times2\times2\times2\times2\times3\times5} \\= 8\sqrt{5\times 3\times 2} \\= 8\sqrt{30}$

now

altitude of the smallest side

smallest side = 8 cm base = 8 cm

area of triangle = $\frac{1}{2}\times base\times height$

$8\sqrt{30} = \frac{1}{2} \times 8 \times h \\h = \frac{8\sqrt{30}\times 2 }{8} \\h = 2\sqrt{30}$

hence the altitude of the smallest side is 2√30

#Learn more:

The sides of a triangle are 11cm ,60cm . Find the altitude of the smallest side

https://brainly.in/question/3895874