1

Problem

In the given figure, with BC: AC = 3:4 and a perimeter of △ACB = 60 cm, where BC equals BD, determine AC, CD, and BA.

2

Step

The given values are

BC = 3 , AC = 4 and perimeter of △ABC = 60 cm

3

Formula

By using the Pythagorean theorem find the AB is \$AB^2 = BC^2 + AC^2\$.

4

Step

Now plug the value in the formula:

\$AB^2 = 3^2 + 4^2\$

\$AB = \sqrt (9 + 16)\$

AB = 5

5

Step

So AB : BC: AC = 5: 3: 4 it can be written as:

△ABC = AB + BC + AC

6

Step

So now find for x value:

60 = 5x + 4x + 3x

60 = 12x

\$x = \cancel(60)^5 / \cancel(12)\$

x = 5

7

Step

Now plug the x value in the AC and make it simpler:

AC = 4x

\$AC = 4 \times 5\$

AC = 20 cm

8

Step

Now plug the x value in the CD and make it simpler:

CD = CB + BD

CD = 2 BC

\$CD = 2 \times 3x\$

\$CD = 2 \times 3 \times 5\$

CD = 30 cm

9

Step

Now plug the x value in the BA and make it simpler:

BA = 5x

\$BA = 5 \times 5\$

BA = 25 cm

10

Solution

So the value of AC, CD , and BA are 20 cm, 30 cm, 25 cm.

11

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

12

Choice-A

This is correct because it matches the calculated values of AC, CD, and BA

Correct AC = 20 cm , CD = 30 cm and BA = 25 cm

13

Choice-B

The provided solution appears to be incorrect as it does not align with the computed values

Wrong AC = 25 cm , CD = 30 cm and BA = 20 cm

14

Choice-C

This choice is inaccurate, as it provides incorrect values for AC, CD, and BA

Wrong AC = 30 cm , CD = 20 cm and BA = 25 cm

15

Choice-D

The solution is inaccurate because it yields inconsistent values for CD and BA

Wrong AC = 20 cm , CD = 25 cm and BA = 30 cm

16

Answer

Option

A

17

Sumup

Please summarize choices