Question

The shortest side of a right triangle is 6 centimeters long. The difference between the lengths of the other two sides is 2 centimeters. Find the missing sides. Use exact values.

A) 4 cm and 10 cm
B) 8 cm and 10 cm
C) 6 cm and 8 cm
D) 4 cm and 8 cm

Answer 1

To find the missing sides of a right triangle, we can use the Pythagorean theorem and solve for the variables. The missing sides in this triangle are 8 cm and 10 cm.

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's assume the missing sides are x and x+2.

Using the Pythagorean theorem, we have:

6^2 + x^2 = (x+2)^2

36 + x^2 = x^2 + 4x + 4

Simplifying the equation, we get:

36 = 4x + 4

4x = 32

x = 8

Therefore, the missing sides are 8 cm and (8+2) cm which simplifies to 8 cm and 10 cm.