Question

The perimeter of a traingular field 240dm if two of its side are 78dm and 50dm find the length of the perpendicular on the side of length 50dm from the opposite vertex?​

Answer 1

Answer:

Perimeter of the triangle = 240 dm

Two sides (given) = 78 dm and 50 dm

Third side of the triangle = 240 - (78 + 50)

= 240 dm - 128 dm

= 112 dm

s = (a + b + c)/2

= (78 + 50 + 112)/2

= 240/2

s = 120 dm

Area of the triangle = √s(s - a)(s - b)(s - c)

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

⇒ √120*70*42*8

⇒ √2822400

Area of the triangle = 1680 sq dm

Now, 

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

Height = 2*area/base

 ⇒ (2*1680)/50 

⇒ 336/5

height = 67.2 dm

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Perimeter of triangle = 240 dm

• Two sides = 78dm and 50dm

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the length of perpendicular ?

Formula to be used :-

• Third side = perimeter -( sum of two sides)

• Area of triangle =√s(s-a)(s-b)(s-c)

•Area of triangle = 1/2 × Base ×Height

• s = (a + b + c)/2

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

We know that,

Perimeter of a triangle = Sum of all sides

Given that,

Two sides = 78dm and 50dm

Now, find the 3rd side of the triangle.

Third side = Perimeter -( Sum of two sides)

= 240 - (78+50)

=240 - 128

= 112 dm

________________________________________________

Now, find the area of given triangle.

We know,

s = (a + b + c)/2

Where,

a = 78

b = 50

c = 112

Put the given values in the formula

⟶ s = (78 + 50 +112)/2

⟶ s = 240/2

⟶ s = 120 dm

Again,

Area of triangle =√s(s-a)(s-b)(s-c)

⠀⠀ ⠀= √ 120(120-78)(120-50)(120-112)

⠀⠀⠀⠀⠀⠀= √120 ×42×70 ×8

⠀⠀⠀⠀⠀⠀= √5040 × 560

⠀⠀⠀⠀⠀ = 1680

Area of triangle = 1680 dm²

_______________________________________________

According to the question, we are asked to find the value of h( Height)

We know,

Area of triangle = 1/2 × Base ×Height ( h)

⠀⠀⠀⠀⠀⠀⟶ 1680 ×2 /50 = h

⠀⠀⠀⠀ ⠀⟶ 3360/50 = h

⠀⠀⠀⠀⠀⠀ ⟶ 336/5 = h

⠀⠀⠀⠀⠀⠀⟶ 67.2 = h

Hence , the height of the triangle = 67.2 dm