Mathematics: = A triangle has sides of lengths 18, 24 and 30 units. What is the length of the shortest altitude of this triangle? Express your answer as a common fraction.

answer: THIS ISNT EVEN A QUESTION...

= A triangle has sides of lengths 18, 24 and 30

Ответ:

20068088

16.03.2022

Mathematics

According to the Heron's formula, Area (A) of the triangle having sides a,b,c units is

s(s−a)(s−b)(s−c)

where

a+b+c

For the given triangle,

a=18 cm

b=24 cm

c=30 cm

18+24+30

=36

36(36−18)(36−24)(36−30)

36×18×12×6

216×216

=216 cm

Smallest side =18 cm

Area of the triangle =

×base×altitude=216

×18× altitude=216

Altitude =

216

=24 cm

Step-by-step explanation:

hope this will help

0,0(0 оценок)

Ответ:

alexvane78

16.03.2022

Mathematics

$\boxed{\boxed{\pink{\bf \leadsto The \ length \ of \ shortest \ altitude \ is \ 2.4\sqrt{6} \ units . }}}$

Step-by-step explanation:

Here given measure of sides are 18 , 24 and 30 units. Firstly let's find the area of ∆ using Heron's Formula.

$\boxed{\red{\bf Area_{\triangle} =\sqrt{s(s-a)(s-b)(s-c)}}}$

Where s is semi Perimeter . And here s will be ( 18 + 24 + 30 ) / 2 = 36 units .

$\bf \implies Area = \sqrt{s(s-a)(s-b)(s-c)}$

$\bf \implies Area = \sqrt{ 36 ( 36 - 18)(36-24)(36-30)}$

$\bf \implies Area = \sqrt{ 36 \times 18 \times 12}$

$\bf \implies Area = \sqrt{ 6^2 \times 6\times 6 \times 2 \times 3}$

$\bf \implies Area = 6^2\sqrt{6} unit^2$

$\bf \boxed{ \implies Area_{triangle} = 36\sqrt{6} units^2}$

Also we know that ,

$\boxed{\red{\bf Area_{\triangle} = \dfrac{1}{2}\times (base)\times (height)}}$

Let's find the altitudes now ,

Altitude on side of 18 units :-

$\bf \implies Area = \dfrac{1}{2} \times (base)(height) \\\\\bf \implies 36\sqrt{6} unit^2 = \dfrac{1}{2} \times 18 \times h_1 = 36\sqrt{6} u^2 \\\\\bf\implies h_1 =\dfrac{ 36\sqrt6 \times 2 }{18} \\\\\boxed{\bf\implies h_1 = 4\sqrt6 units }$

Altitude on side of 24 units :-

$\bf \implies Area = \dfrac{1}{2} \times (base)(height) \\\\\bf \implies 36\sqrt{6} unit^2 = \dfrac{1}{2} \times 24 \times h_1 = 36\sqrt{6} u^2 \\\\\bf\implies h_1 =\dfrac{ 36\sqrt6 \times 2 }{24} \\\\\boxed{\bf\implies h_1 = 3\sqrt6 units }$

Altitude on side 30 units :-

$\bf \implies Area = \dfrac{1}{2} \times (base)(height) \\\\\bf \implies 36\sqrt{6} unit^2 = \dfrac{1}{2} \times 30 \times h_1 = 36\sqrt{6} u^2 \\\\\bf\implies h_1 =\dfrac{ 36\sqrt6 \times 2 }{30} \\\\\boxed{\bf\implies h_1 = 2.4\sqrt6 units }$

Hence the lenght of shortest altitude is 2.4√6 units and its on the side of 30 units.

0,0(0 оценок)

= A triangle has sides of lengths 18, 24 and 30 units. What is the length of the shortest altitude of this triangle? Express your answer as a common fraction.

Ответ:

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question