Answer:
[tex]A = 4[/tex]
[tex]B = 6[/tex]
Step-by-step explanation:
Let the two sides be A and B, such that:
[tex]A = \frac{2}{3} * B[/tex]
[tex]Perimeter = 20cm[/tex]
Required
Find A and B
The perimeter is calculated as:
[tex]Perimeter = 2 * (A + B)[/tex]
Substitute [tex]\frac{2}{3} * B[/tex] for A and 20 for Perimeter
[tex]20 = 2 * (\frac{2}{3} * B + B)[/tex]
[tex]20 = 2 * (\frac{2B}{3} + B)[/tex]
Divide both sides by 2
[tex]10 = \frac{2B}{3} + B[/tex]
Multiply both sides by 3
[tex]3 * 10 = 3 * (\frac{2B}{3} + B)[/tex]
[tex]30 = 2B + 3B[/tex]
[tex]30 = 5B[/tex]
Solve for B
[tex]B = \frac{30}{5}[/tex]
[tex]B = 6[/tex]
Recall that:
[tex]A = \frac{2}{3} * B[/tex]
[tex]A = \frac{2}{3} * 6[/tex]
[tex]A = 2 * 2[/tex]
[tex]A = 4[/tex]
Hence, the lengths of the sides are 4 cm and 6 cm
