In the given figure, BC: AC = 3:4 and perimeter of △ABC = 60 cm. Determine AC, CD, and BA.

The given values are

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

By using the Pythagorean theorem find the AB

\$"AB"^2 = "BC"^2 + "AC"^2\$

Now plug the values in the formula

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

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

AB = 5

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

△ABC = AB + BC + AC

So now find for x value

60 = 5x + 4x + 3x

60 = 12x

x = 5

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

AC = 4x

\$"AC" = 4 times 5\$

AC = 20cm

Now plug the x value in the CD and make it simpler
(i,e., BD = BC)

CD = CB + BD

\$"CD" = 2 "BC"\$

\$"CD" = 2 times 3"x"\$

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

CD = 30cm

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

\$"BA" = 5"x" \$

\$"BA" = 5 times 5\$

BA = 25cm

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

Can you summarize what you’ve understood in the above steps?

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

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

This is not correct because it doesn’t match the calculated values

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

Incorrect calculation. Wrong values for AC, CD, and BA

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

This is not correct because it provides different values for CD and BA

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

Option

A

Can you summarize what you’ve understood in the above steps?