# Triangle has sides $5cm,{\text{ }}12cm,$ and $13cm$. Find the length of the perpendicular from the opposite vertex to the side whose length is $13cm$.

Last updated date: 20th Mar 2023

•

Total views: 305.1k

•

Views today: 7.84k

Answer

Verified

305.1k+ views

**Hint:**In this question we will use the area of the right angle triangle that is half multiplied by its base and perpendicular, by considering the other base and perpendicular of the same triangle then we will equate both areas.

**Complete step-by-step answer:**

Let $AB = 5cm,{\text{ }}BC = 12cm,{\text{ }}CA = 13cm$

So, these sides makes a right angle triangle because

$

{\left( {CA} \right)^2} = {\left( {AB} \right)^2} + {\left( {BC} \right)^2} \\

{13^2} = {5^2} + {12^2} = 169 = {13^2} \\

$

Therefore ABC is a right angle triangle at B

Let BD be the perpendicular on side AC

Let $BD = xcm$

From figure the area of right angle triangle is half multiply by perpendicular time’s base

\[

\Delta ABC = \dfrac{1}{2}\left( {AB} \right)\left( {BC} \right) = \dfrac{1}{2}\left( {BD} \right)\left( {AC} \right) \\

= \dfrac{1}{2}\left( 5 \right)\left( {12} \right) = \dfrac{1}{2}\left( x \right)\left( {13} \right) \\

\Rightarrow 60 = 13x \\

\Rightarrow x = \dfrac{{60}}{{13}}cm \\

\]

So, this is the required perpendicular distance from the opposite vertex to the side whose length is $13cm$.

**Note:**In such types of questions first draw the pictorial representation of the given problem, then check whether it is right angle triangle or not if it is then using the formula of area of triangle which is half multiply by perpendicular time’s base, then we can easily calculated the length of the perpendicular from the opposite vertex to the side whose length is $13cm$.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE