Question

the drawing below shows a side view of a picture frame on marys desk.

image of a right triangle with height 16 cm and base 4.2 cm, and the hypotenuse labeled support

which of the following is closest to the length of the frame support?
a 20 cm
b 15 cm
c 12 cm
d 17 cm

Explanation:

Step1: Identify the triangle type

The support, the height (16 cm), and the horizontal segment (4.2 cm) form a right triangle. So we can use the Pythagorean theorem, \( c = \sqrt{a^2 + b^2} \), where \( a = 16 \) and \( b = 4.2 \).

Step2: Calculate \( a^2 \) and \( b^2 \)

First, calculate \( 16^2 = 256 \) and \( 4.2^2 = 17.64 \).

Step3: Sum the squares

Add them together: \( 256 + 17.64 = 273.64 \).

Step4: Take the square root

Find the square root of 273.64: \( \sqrt{273.64} \approx 16.54 \), which is closest to 17 cm.

Answer:

D. 17 cm