The perimeter of the rectangle is 26cm. Find its sides if you know that the area of the triangle is 36cm2.

Let’s express one of the size of our shape, for which we will use the variable a.

Then another size of our figure can be represented as 26: 2 – a = 13 – a.

Since we know from the condition of the task that the area of our figure is 36 cm2, then we write down the equation and find out what are the lengths of its sides:

a * (13 – a) = 36;

13a – a ^ 2 – 36 = 0;

a ^ 2 – 13a + 36 = 0;

D = 169 – 4 * 36 = 25 = 52;

a1 = (13 + 5): 2 = 9;

a2 = (13 – 5): 2 = 4.

Answer: Width 9 centimeters, length 4 centimeters, or vice versa.