Answer:
31. x = √52
32. x = 5√2
Step-by-step explanation:
31. Draw a line from the top right corner straight down to the extended line. This forms a 30-60-90 triangle. Since the hypotenuse is 4 cm, the height is 2 cm, and the width is 2√3 cm.
Therefore, if we look at the overall right triangle, the height is 2 cm, the width is 4√3 cm, and the hypotenuse is x cm. Using Pythagorean theorem:
c² = a² + b²
x² = (2)² + (4√3)²
x² = 4 + 48
x = √52
32. Draw a line from the top point straight down to the base. This splits the bottom triangle into a 30-60-90 triangle and a 45-45-90 triangle.
The hypotenuse of the 30-60-90 triangle is 10 cm, so the base is 5 cm, and the height is 5√3 cm.
The height of the 45-45-90 triangle is 5√3 cm, so the hypotenuse is 5√6 cm.
Now if we look at the 30-60-90 triangle on the right, its height is 5√6 cm, so its base is 5√2 cm.
