Question

The perimeter of a triangular field is 240m. One side is 78m & another side is 50m. Find the third side and the length of the altitude from side 50 m to the opposite vertex.
please help me

Answer 1

The value of 3 side is 112m.

Now for the altitude u need to take base as 50 m .

So area of triangle is 1/2*b*h .

Area=1/2*b*h

Here we know base that is 50 but we need to find area of triangle . So find the area of triangle by heron’s formula and put it’s value in above equation and u eill get your ans.

Answer 2

AnSwer -:


Height of triangle-: 67.2 m

Third side of a triangle-: 112 m

_______________________________


_____________________________

Explanation-:

Area of triangle using sides -:

“ A= √[s(s-a)(s-b)(s-c)]”

S = semi perimeter

A =Area

A,B,C = three sides of triangle

Area of triangle using base and height-:

“A = 1/2 x b x h”

A = Area

B = Base

H = height

______________________________

Given ,

Perimeter of triangle =240 m,

Two sides are 78m and 50 m

To find ,

The third side of triangle

The altitude of the triangle

______________________________

Now ,

Third side of a triangle-:

Perimeter of triangle - sum of two sides

of a triangle


Perimeter of triangle =240 m,

Two sides are 78m and 50 m = 128m

Then,

= 240 dm - 128 m

= 112 m

Therefore,

Third side of a triangle-: 112 m

Now ,

Semi perimeter of triangle-:

s = (a + b + c)/2

= (78 + 50 + 112)/2

= 240/2

s = 120 m

Semi perimeter = 120 m

“ A= √[s(s-a)(s-b)(s-c)]”

S = semi perimeter = 120 m

A =Area =??

A = 78 m

B = 50 m

C = 112 m

⇒ √120 (120 - 50)(120 - 78)(120 - 112)


⇒ √120 x 70x 42 x 8

⇒ √2822400

Area of the triangle = 1680 sq m


Now ,

Area of the triangle = 1/2 x base x height

Height = 2 x area/base


Height = 2 x area/base

⇒ (2 x 1680)/50

⇒ 336/5

height = 67.2 m

Hence ,

Height of triangle-: 67.2 m

_______________________________