Geometric Mean and Pythagorean Theorem

The accompanying diagram shows a 24-foot ladder leaning against a building. A steel brace extends from the ladder to the point where the building meets the ground. The brace forms a right angle with the ladder.If the steel brace is connected to the ladder at a point that is 10 feet from the foot of the ladder, which equation can be used to find the length, x, of the steel brace?

• 4

• 2√6

• 6√2

• 12

What is the missing side length for the triangle shown?

• 17 cm

• 13 cm

• 7 cm

• 18 cm

What is the value of x in the triangle shown?

• 16 in.

• 32 in.

• 8 in.

• 4√2

What is the value of x for the triangle shown?

• 3√22 cm

• 23 cm

• 4√3 cm

• 15 cm

The diagram shows a right triangle and the lengths of two of its sides in inches. What is the measurement of d in inches?

Round to the nearest tenth of an inch.

Mathematical Equivalence

ON

What is the value of x in the triangle shown?

• 4√2 cm

• 4 cm

• √20 cm

• 7 cm

Find the value of w.

• w = 144

• w = 36

• w = 3

Find the value of y. *Hint: You need to find x first.*

• 5

• 10√30

• √300

• 10√3

Find the value of x.

• 15√5

• 5√5

• 5√3

• 3√5