The shortest side of a right triangle is 14 inches long. The difference between the lengths of the other two sides is 2 inches. Find the missing sides. Use exact values.

The missing sides are 50 inches and 48 inches long.

Step-by-step explanation:

Let the lengths of the other two sides be x inches and y inches

And let x represent the length of the longest side.

From the question,

The difference between the lengths of the other two sides is 2 inches. That is,

x - y = 2 (1)

The three sides of the right triangle are x, y, and 14 inches long.

From the Pythagorean theorem, " In a right triangle, the square of the longest side equals sum of squares of the other two sides"

Here, the longest side is x

Hence, we can write that

x² = y² + 14²

∴ x² = y² + 196 (2)

Now, we have two equations, we can then solve simultaneously.

From equation (1)

x - y = 2

∴ x = y + 2 (3)

Put this into equation (2)

x² = y² + 196

(y+2)² = y² + 196

y² + 4y + 4 = y² + 196

4y + 4 = 196

4y = 196 - 4

4y = 192

y = 192/4

y = 48

To determine x, we will substitute the value of y into equation (3)

x = y + 2

∴ x = 48 + 2

x = 50

Hence, x = 50 and y = 48

Since the lengths of the other two sides are x inches and y inches,

Hence, the missing sides are 50 inches and 48 inches.

mxb67

step-by-step explanation: