1

Problem

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

2

Step

Given

Base (b) = 8 cm, side (a) = 6cm, 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) is \$(a + b + c)/2\$.

5

Step

Substitute the values in the semi -perimeter formula:

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

s = \$(18)/2 cm\$

s = 9cm

6

Hint

Therefore, s value is 9 cm.

7

Step

Plug the values into Heron’s formula:

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

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

8

Step

After Simplification:

\$\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

The calculation under Heron’s formula does not simplify to 132. It is incorrect as 135 > 132

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

12

Choice-B

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

Wrong \$\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

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

14

Choice-D

Like the others, this is incorrect because it does not match the exact result from Heron’s formula. The correct result is \$\sqrt(135)\$

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

15

Answer

Option

C

16

Sumup

Please summarize choices