Question

The sides of a triangle are 25cm 17cm 12cm find the length of the altitude on the longest cm This question is from herons formula

Answer 1

Step-by-step explanation:

7.2cm is the right answer

Answer 2

$\bf {\huge {\underline {\boxed {\sf {\purple {Answer:\:7.2\:cm}}}}}}$

$\textbf {\underline {\underline {Step-By-Step\:Explanation:-}}}$

$\textbf {\underline {\blue {Given:}}}$

• Sides of triangle = 25 cm, 17 cm and 12 cm

$\textbf {\underline {\blue {To\:Find:}}}$

• Altitude on the longest cm

$\huge\underline\green {\tt Solution:}$

Let a = 25 cm, b = 17 cm and c = 12 cm

Semi- Perimeter = $\dfrac {Perimeter}{2}$

S = $\dfrac {25 + 17 + 12 }{2}$

S = $\dfrac {54}{2}$

S = 27 cm

Now,

•°• Area of Triangle =

$\sqrt {S(S-a)(S-b)(S-c)}$

= $\sqrt {27(27-25)(27-17)(27-12)}$

= $\sqrt {27(2)(10)(15)}$

= $\sqrt {8100}$

= 90

•°• Area of given triangle is 90 $cm^2$

Now,

Longest side of the triangle = 25 cm

➡ Area of triangle = $\dfrac {1}{2}$ × Base × height ( Altitude )

➡ 90 = $\dfrac {1}{2}$ × 25 × Altitude

➡ Altitude = $\dfrac {90 × 2 }{25}$

•°• Altitude = 7.2 cm

Hence,

Altitude of the given triangle is 7.2 cm