The perimeter of the triangle is 32 cm, and its area is 60 cm. Find the sides of the rectangle.

Let’s say that the length of the figure is a cm, while the width is in cm.

We get the following system of equations:

2 * (a + b) = 32 cm.

a * b = 60 cm2

Express the sum of the width and length values from the first equation.

a + b = 32/2.

a + b = 16.

We express the value of a.

a = 16 – c.

Substitute the value a into the second equation.

(16 – in) * in = 60.

16 * in – in ^ 2 – 60 = 0.

b ^ 2 – 16 * b + 60 = 0.

On the Vieta’s tower we get:

a = 10 cm.

h = 6 cm.

Examination:

2 * (10 + 6) = 2 * 16 = 32 cm.

10 * 6 = 60 cm2

Answer:

10 and 6 cm.