Answer:
The missing sides are 50 inches and 48 inches long.
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.