Question

The length of largest of the altitudes of the triangle with sides 12 cm, 16 cm and 20 cm, is

Answer 1

Answer:

Area of triangle with sides a, b,and c and s =

2

a+b+c

is

s(s−a)(s−b)(s−c)

.

For triangle with sides 16 cm, 12 cm and 20 cm, s=

2

16+12+20

=24cm

Area of the triangle with sides 16 cm, 12 cm and 20 cm =

24(24−16)(24−12)(24−20)

=

24×8×12×4

=

8×3×8×4×3×4

=8×3×4=96cm

2

Area of triangle can also be calculated using the formula

2

1

×base×height

Let the height for base 12cm, be h.

So, area =

2

1

×12×h=96cm

2

=>h=16cm

Answer 2

Answer: 16 cm

Step-by-step explanation:
We will use Heron's Formula
So, Semi-perimeter = 12+16+20/2 = 24 cm
∵A =$\sqrt{24(24-12)(24-16)(24-20)} =\sqrt{9216} = 96cm^{2}$
As we need the largest altitude we need to take the smallest base i.e. 12cm.
So, 1/2 ×12×h = 96
After solving we get h as 16 cm
∴The answer is 16cm.