Question

The perimeter of a right-angle triangle is 56 cm, and the area is 84 cm^2. Find the sides of the triangle.

A) 7 cm, 24 cm
B) 14 cm, 28 cm
C) 12 cm, 20 cm
D) 6 cm, 18 cm

Answer 1

To determine the sides of the right-angle triangle, equations based on the perimeter and area are derived and solved using the properties of right triangles, including the Pythagorean theorem. The correct dimensions that satisfy the given perimeter and area must be derived from these relations.

Step-by-step explanation:

To find the sides of a right-angle triangle with a perimeter of 56 cm and an area of 84 cm2, we can use the information given and derive equations based on the properties of right triangles. Since the triangle is right-angled, we can denote the sides as a, b, and c, where c is the hypotenuse, so the perimeter is a + b + c = 56 cm.

Also, the area is (1/2) × a × b = 84 cm2, giving us a second equation. We know from the Pythagorean theorem that a2 + b2 = c2. Now we have two variables and two equations:

1. a + b + c = 56 cm (perimeter)
2. (1/2) × a × b = 84 cm2 (area)

Substituting c=56-a-b into a2 + b2 = c2, we have a quadratic equation that we can solve for a and b. Testing the given options with these constraints will lead us to the correct dimensions of the sides.