8 Geometric meanPAPER SIZES. International standard paper sizes are commonly used all over the world. The various sizes all have the same width-to-length ratios. Two sizes of paper are shown, called A4 and A3. The distance labeled x is the geometric mean of 210 mm and 420 mm. Find the value of x.
9 Write proportion 210 x = x 420 X2 = 210 ∙ 420 X = √210 ∙ 420 X = 297mm Solution:210xWrite proportion=x420X2 = 210 ∙ 420X = √210 ∙ 420X = 297mmCross product propertySimplify
11 Find the positive square root. EXAMPLE 1Find the length of a hypotenuseFind the length of the hypotenuse of the right triangle.(hypotenuse)2= (leg)2 + (leg)2Pythagorean Theoremx2 =Substitute.x2 =Square.x2 = 100Add.x = 10Find the positive square root.
12 GUIDED PRACTICEfor Example 11.Find the unknown side length of the right triangle. Write your answer in simplest radical form.ANSWER4
13 GUIDED PRACTICEfor Example 1Find the unknown side length of the right triangle.2.13ANSWER