Question

4.) If the two sides of a triangle are 13 cm and 17 cm and the perimeter of triangle 50 cm what will be the length of third side. *
20 cm
25 cm
15 cm
22 cm​

Answer 1

Answer:

20cm

Step-by-step explanation:

13+17=30

50-30=20

Answer 2

Step-by-step explanation:

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 =$\frac{13 + 17 + 20}{2}</p><p> </p><p> </p><p>s =[tex] \frac{50}{2}s= </p><p>2</p><p>50</p><p> </p><p> </p><p>s = 25s=25$

$\sqrt{s(s-a)(s-b)(s-c)} </p><p>s(s−a)(s−b)(s−c)$

$= \sqrt{25(25-13)(25-17)(25-20)}= </p><p>25(25−13)(25−17)(25−20)$

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

25∗12∗8∗5[/tex]

$= \sqrt{12000}=$

12000[/tex]

$= 20\sqrt{30}=20$

30[/tex]

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.