In a right-angled triangle, whose area is 42 cm square, the sum of the lengths of the legs is 15.5 cm.

In a right-angled triangle, whose area is 42 cm square, the sum of the lengths of the legs is 15.5 cm. What is the hypotenuse.

The area of a right-angled triangle is equal to: Savs = AB * AC / 2.

AB * AC = 2 * Savs = 2 * 42 = 84 cm2. (one).

By condition, AB + AC = 15.5 cm. (2).

Let’s solve the system of equations 1 and 2.

AB = 15.5 – AC.

(15, 5 – AC) * AC = 48.

15.5 * AC – AC ^ 2 = 48.

AC ^ 2 – 15.5 * AC + 48 = 0.

D = b ^ 2 – 4 * a * c = (-15.5) ^ 2 – 4 * 1 * 84 = 240.25 – 336 = -95.75.

Since D <0, the equation has no roots, therefore, such a triangle does not exist.

With an area of 21 cm2. AC = 3.5 cm, AB = 12 cm.

Answer: The triangle does not exist.