Question

The perimeter of a triangle is 36 cm. If the altitudes of the triangle are
in ratio 1:2 : 3 then find the length of the corresponding sides of the
triangle.​

Answer 1

Answer:

AB=6cm, BC=12 cm, AC=18cm.

Step-by-step explanation:

let the sides of triangle are in the ratio be x

then side be x, 2x, 3x

by putting the formula if perimeter of triangle x= 6cm .

first side =6cm,second side =12cm,third side = 18 cm

Answer 2

$a=19.6 cm,b=9.8 cm.c=6.5 cm$

Step-by-step explanation:

Let sides of triangle are a, b and c

Perimeter of triangle =36 cm

a+b+c=36

Let length of altitude drawn on side a=x

Length of altitude drawn on side b=2x

Length of altitude drawn on side c=3x

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

Using the formula

Area of triangle=$\frac{1}{2}\times x\times a=\frac{ax}{2}$ square cm

Area of triangle=$\frac{1}{2}\times 2x\times b=\frac{2xb}{2}$square cm

Area of triangle=$\frac{1}{2}\times 3x\times c=\frac{3xc}{2}$square cm

$\frac{ax}{2}=\frac{2xb}{2}=\frac{3xc}{2}$

$a=2b=3c$

$b=\frac{a}{2},c=\frac{a}{3}$

Substitute the values

$a+\frac{a}{2}+\frac{a}{3}=36$

$\frac{6a+3a+2a}{6}=36$

$11a=36\times 6=216$

$a=\frac{216}{11}=19.6 cm$

$b=\frac{a}{2}=\frac{19.6}{2}=9.8 cm$

$c=\frac{19.6}{3}=6.5 cm$

#Learns more:

https://brainly.in/question/14330652:Answered by Priyanshi