1

Problem

Find the area of the scalene triangle ABC with the sides 8 cm, 6 cm, and 4 cm.

2

Step

Given that

Base (b) = 8 cm, side (a) = 6 cm, and c = 4 cm

3

Formula

Heron’s formula states that the area A of a triangle with sides a, b, and c is given by: A = \$\sqrt(s \times (s - a) \times (s - b) \times (s - c)\$

4

Formula

Calculate the semi-perimeter(s) formula is \$(a+b+c)/2\$.

5

Step

Substitute the values in the semi- perimeter formula:

s = \$(6 + 8 + 4)/2\$

s = \$(18)/2\$

s = 9 cm

6

Step

Therefore, s value is 9 cm.

7

Step

Substitute the values into Heron’s formula:

A = \$\sqrt(9 \times (9 - 6) \times (9 - 8) \times (9 - 4)\$

A = \$\sqrt(9 \times 3 \times 1 \times 5)\$

8

Step

After Simplication we get,

\$\sqrt(27) \times (5)(cm)^2\$

A = \$\sqrt(135)(cm)^2\$

9

Solution

Therefore, the area of scalene triangle is \$\sqrt(135)(cm)^2\$.

10

Sumup

Please summarize steps

Choices

11

Choice-A

It is incorrect because \$\sqrt(132)\$ is not equal to the calculated area \$\sqrt(135)\$

Wrong \$\sqrt(132) cm^2\$

12

Choice-B

It is incorrect because \$\sqrt(134)\$ is not equal to the calculated area \$\sqrt(135)\$

Correct \$\sqrt(134) cm^2\$

13

Choice-C

It is correct because \$\sqrt(135)\$ is equal to the calculated area using Heron’s formula for the given scalene triangle

Wrong \$\sqrt(135) cm^2\$

14

Choice-D

It is incorrect because \$\sqrt(133)\$ is not equal to the calculated area \$\sqrt(135)\$

Wrong \$\sqrt(133) cm^2\$

15

Answer

Option

B

16

Sumup

Please summarize choices