Question

The perimeter of a triangle is 50 cm. One side of the triangle is 4 cm
longer than the smallest side and the third side is 6 cm less than twice
the smallest side. Find the area of the triangle​

Answer 1

Answer:

Step-by-step explanation:

Define x:

Let the smallest side be x

2nd side = x + 4

3rd side = 2 x - 6

The perimeter is 50 cm:

x + (x + 4) + (2 x - 6) = 50

x + x + 4 + 2 x - 6 = 50

4 x - 2 =50

4 x = 52

x = 13 cm

Find the sides:

Side 1 = x = 13 cm

Side 2 = x + 4 = 13 + 4 = 17 cm

Side 3 = 2 x - 6 = 2(13) - 6 = 20 cm

Find the area:

area = √p(p-a)(p-b)(p-c)

p = 50 ÷ 2 = 25

area = √25(25 - 13)(25 - 17) (25 - 20)

area = √25(12)(8)(5)

area = √12000

area = 20√30 or ≈ 110 cm²

Hope it helps you.

Hope it helps you.

Answer 2

Answer:

Let the Length of the smaller side = x cm

Length of the second side = (x + 4) cm

Length of the third side = (2x - 6) cm

Perimeter of a Triangle = 50 cm

According to Question now,

➳ Perimeter of triangle = Sum of all sides

➳ 50 = x + (x + 4) + (2x - 6)

➳ 50 = x + x + 4 + 2x - 6

➳ 50 = 4x - 2

➳ 4x = 50 + 2

➳ x = 52/4

➳ x = 13

Therefore,

Length of the smaller side = x = 13 cm

Length of the second side = (x + 4) = 13 + 4 = 17 cm

Length of the third side = (2x - 6) = 2(13) - 6 = 26 - 6 = 20 cm

_____________________

Now, we will find the Semi Perimeter of triangle :

Let a = 13 cm, b = 17 cm = c = 20 cm

➳ S = a + b + c/2

➳ S = 13 + 17 + 20/2

➳ S = 50/2

➳ Semi Perimeter = 25 cm

Now, we will find the area of triangle by using herons Formula :

$: \implies \sf \: Area = \sqrt{s(s - a) \: (s - b) \: (s - c) }$

$: \implies \sf \: Area = \sqrt{25(25 - 13) \: (25 - 17) \: (25- 20) }$

$: \implies \sf \: Area = \sqrt{25 \times 12 \times 8 \times 5 }$

$: \implies \sf \: Area = \sqrt{12000 }$

$: \implies \underline{ \boxed{ \sf \: Area = 20\sqrt{30 } \: cm }}$