Question

the perimeter of a triangle is 5 centimetre one side is the triangle is 4 cm length then the smallest side and third side is 6 less than the smallest side find the area of the triangle​

Answer 1

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}

s = \frac{50}{2}

s = 25

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

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

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

= \sqrt{12000}

= 20\sqrt{30}

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

∴ 20 \sqrt{30} cm^{2} or 109.54451 cm^{2} is the area of the triangle.

Hope this may help you.