Question

The sides of triangle are in the ratio 13: 14: 15 and it's perimeter is 294 cm calculate its area and the length of the altitude on the longest side

Answer 1

Step-by-step explanation:

Let the sides of the triangle be 13x, 14x and 15x

where a=13x, b= 14x and c= 15x

According to question,

Perimeter of the triangle =13x+14x+15x

294=42x

294/42=x

x=7

13x= 13*7=91

14x=14*7=98

15x=15*7=105

So, the sides of the ∆ are 91, 98 and 105

Therefore, s= 91+98+105/2

By using Heron's formula,we get

Area of ∆= √s(s-a)(s-b)(s-c) ( solve using this formula)

After that

area = 1/2 * base( it has the shortest side in a ∆) * height( it's size is lesser than hypotenuse but it is bigger than base)

Solve the rest of the sum, if you have any doubt I am here to clear it out, just comment on my answer

Answer 2

Area of triangle=   $A =4116cm^{2}$    Length of altitude=$h=78.4cm$  

Step-by-step explanation:

Given,

Sides of a triangle in the ratio are 13:14:15

Perimeter of triangle =294 cm

Solution,

Let sides of triangle are $13x,14x,15x$

$a=13x, b=14x ,c=15x$

Perimeter of triangle=a+b+c

$p=13x+14x+15x=294$

$42x=294$

$x=294/42$

$x=7$

Sides of a triangle are

$a=13\times 7=91cm$

$b=14\times 7=98cm$

$c=15\times 7=105cm$

Semi perimeter of triangle $s=(a+b+c)/2$

$s=294/2=147cm$

Area of triangle by Herons formula

$Area=\sqrt{s\left ( s-a \right )\left ( s-b \right )\left ( s-c \right )}$

         $=\sqrt{147\left ( 147-91 \right )\left ( 147-98 \right )\left ( 147-105 \right )}$

          $=\sqrt{147\times 56\times 49\times 42}$

           $=4116cm^{2}$  

Area of triangle $A=1/2\times base\times height$

If base is longest side then calculate altitude on longest side.

Let altitude is h

$4116=1/2\times 105\times h$

$h=4116\times 2/105$

$h=78.4cm$