Question

calculate the are of triangle whose sides are 13cm,5cm,and 12cm.calculate the altitude using longest side as base .leave your answer as fraction

Answer 1

Answer:

• Altitude of triangle is 60/13 cm.

Step-by-step explanation:

We will use Heron's formula here, beacuse we do not have height of triangle.

Heron's formula is '

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

Where,

• s is semi-perimeter of triangle.
• a, b and c are sides of triangle.

Semi - Perimeter of triangle = Perimeter/2

$\longrightarrow$ Semi-perimeter = 13 + 5 + 12/2

$\longrightarrow$ Semi-perimeter = 30/2

$\longrightarrow$ Semi-perimeter = 15

Semi-perimeter of triangle is 15 cm.

We will find area :

$\longrightarrow$ Area = √15(15 - 13)(15 - 5)(15 - 12)

$\longrightarrow$ Area = √15 × 2 × 10 × 3

$\longrightarrow$ Area = √5 × 3 × 2 × 2 × 5 × 3

$\longrightarrow$ Area = 2 × 3 × 5

$\longrightarrow$ Area = 30

Area of triangle is 30 cm².

Now,

Let, Height/altitude of triangle be h.

13 cm is longest side of triangle. So, If we take base 13 cm and height/altitude of triangle be h then area of triangle will same.

So,

Area of triangle = ½ × base × height

$\longrightarrow$ 30 = ½ × 13 × h

$\longrightarrow$ 30 × 2 = 13 × h

$\longrightarrow$ 60 = 13 × h

$\longrightarrow$ 60/13 = h

Altitude of triangle is 60/13 cm.

Answer 2

Answer:

Area = 30$cm^{2}$ | Altitude = 4cm

Step-by-step explanation:

Semi-perimeter of triangle= s = (13+5+12)/2

                                                 = 30/2

                                                 = 15cm

Area = $\sqrt{(s)(s-13)(s-5)(s-12)}$ (Heron's Formula)

        = $\sqrt{(15)(15-13)(15-5)(15-12)}$

        = $\sqrt{(15)(2)(10)(3)}$

        = $\sqrt{(5)(5)(3)(3)(2)(2)}$

        = 5×3×2

        = 30$cm^{2}$

Altitude of triangle according to longest side = area/longest side*1/2

                                                                           = 30/7.5

                                                                           = 4cm