Find the area of a triangle whose sides are 9 cm, 28 cm, and 35 cm.

i am getting the answer has 2304 root 3 but in examples it is showing 36 root 6

Question

Find the area of a triangle whose sides are 9 cm, 28 cm, and 35
cm
i am getting the answer has 2304 root 3 but in examples it is
showing 36 root 6

Pooja · Accepted Answer

The sides are given to be 9cm, 28cm and 35cm.

So, as per Heron's formula,

Semi-perimeter,

$s = \frac{s u m o f t h r e e s i d e s o f t h e t r i a n g l e}{2} = \frac{9 + 28 + 35}{2} = \frac{72}{2} = 36$

Thus,

Area of triangle =

$\sqrt{s (s - a) (s - b) (s - c)} = \sqrt{36 (36 - 9) (36 - 28) (36 - 35)} = \sqrt{36 \times 27 \times 8 \times 1} = \sqrt{(2 \times 2 \times 3 \times 3) \times (3 \times 3 \times 3) \times (2 \times 2 \times 2) \times 1}$

Now, making pairing different prime factors in a group of two, we get

$2 \times 2 \times 3 \times 3 \times \sqrt{2 \times 3} = 36 \sqrt{6} {c m}^{2}$

This is how we get $36 \sqrt{6} {c m}^{2}$ as our answer.

Find the area of a triangle whose sides are 9 cm, 28 cm, and 35 cm. i am getting the answer has 2304 root 3 but in examples it is showing 36 root 6

Find the area of a triangle whose sides are 9 cm, 28 cm, and 35 cm.

i am getting the answer has 2304 root 3 but in examples it is showing 36 root 6