Answer:
x = 7√2 ≈ 9.90
Explanation:
You want the hypotenuse of an isosceles right triangle with one leg given as 7 units.
Special triangles
An isosceles right triangle is a "special triangle." Its side lengths have the ratios ...
1 : 1 : √2
Multiplying this set of numbers by 7, we see the longest side is 7√2:
7 : 7 : 7√2
The value of x is 7√2 ≈ 9.90.
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Additional comment
If you like, you can figure this using the Pythagorean theorem. You know the triangle is isosceles because the sum of angles is 180°. The missing angle (at lower right) is ...
180° -90° -45° = 45°
This is the same as the one shown, so the other short side will have the same measure as the one shown: 7 units.
The Pythagorean theorem tells you ...
x² = 7² +7² = 7²·2
x = √(7²·2)
x = 7√2
The other "special triangle" is the right triangle with angles 30°, 60°, 90°. The ratios of its side lengths are 1 : √3 : 2. This is another triangle you will see often in algebra, geometry, and trig problems.
These right triangles are "special" because both their angles and some of their trig functions have rational values. There aren't any other right triangles having that property.