Question

The Perimeter of a triangle is 50 m. one side of triangle is 4 m longer than the smaller side and third side is 6m less than the twice the smaller side find area of triangle​

Answer 1

Answer:

Perimeter of triangle = 50 cm

Let the length of the smaller side be x cm.

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

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

Sum of lengths of triangle = Perimeter

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

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

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

4x - 2 = 50

4x = 50 + 2

x = 52/4 = 13

x = 13

Length of the first side = x cm = 13 cm

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

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

FINDING OUT THE AREA OF THE TRIANGLE USING HERON'S FORMULA

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

s = \frac{a+b+c}{2}s=

2

a+b+c

s = \frac{13 + 17 + 20}{2}s=

2

13+17+20

s = \frac{50}{2}s=

2

50

s = 25s=25

\sqrt{s(s-a)(s-b)(s-c)}

s(s−a)(s−b)(s−c)

= \sqrt{25(25-13)(25-17)(25-20)}=

25(25−13)(25−17)(25−20)

= \sqrt{25 * 12 * 8 * 5}=

25∗12∗8∗5

= \sqrt{12000}=

12000

= 20\sqrt{30}=20

30

I have just simplified the square root as it is a surd.

∴ 20 \sqrt{30}20

30

cm^{2}cm

2

or 109.54451 cm^{2}cm

2

is the area of the triangle.

Hope this may help you.

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Answer 2

Step-by-step explanation:

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 :

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

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

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

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

$: \implies \underline{ \boxed{ \sf \: Area = 20\sqrt{30 } \: cm^2 }}$