The perimeter of the rectangle is 20cm. Find its sides if you know that the area of the rectangle is 24cm ^ 2.

1) Let a cm – the length of the rectangle, b cm – its width.

2) (2a + 2b) cm – the perimeter of this rectangle, equal to 20 cm:

2a + 2b = 20.

3) (a * b) cm ^ 2 – the area of a rectangle equal to 24 cm ^ 2:

a * b = 24.

4) From the equation 2a + 2b = 20 we express the value of a:

a + b = 10;

a = 10 – b.

5) Then

(10 – b) * b = 24;

10b – b ^ 2 – 24 = 0;

b ^ 2 – 10b + 24 = 0.

Solving the quadratic equation, we find that x1 = 6, x2 = 4.

6) This means that the length of the rectangle is either 6 cm or 4 cm.

7) Find the width of the rectangle:

b = 24: 6 = 4 cm

or

b = 24: 4 = 6 cm.

Answer: 6 and 4 cm.




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