9
1) In this right triangle we can find the missing leg by using the Pythagorean Theorem.
2)
a² = b² + c² Note that the hypotenuse is unknown so far
a² = 7² + (4√2)²
a² = 49 +(16 x2)
a² = 49 +32
a² =81 Take the square root on both sides
√a² = √81
a = -9, 9 Negative numbers for dimensions are not convenient.
a = 9
3) Hence, the answer is 9