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.

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?