Question

select the correct answer. a triangular tabletop has the given dimensions. vinyl is placed around the outer edges of the tabletop. what is the approximate length of vinyl needed for the outer edges of the tabletop? a. 10.2 ft b. 11.2 ft c. 9 ft d. 14.2 ft

Explanation:

Step1: Identify the triangle type

The triangle is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are congruent. Let the length of each leg be $a$ and the hypotenuse be $c$. Given one leg $a = 3$ ft.

Step2: Use the Pythagorean theorem or the 45 - 45 - 90 triangle ratio

For a 45 - 45 - 90 triangle, the ratio of the sides is $a:a:c=1:1:\sqrt{2}$. So if $a = 3$ ft, the hypotenuse $c=a\sqrt{2}=3\sqrt{2}\approx3\times1.414 = 4.242$ ft.

Step3: Calculate the perimeter

The perimeter $P$ of the triangle is the sum of the lengths of its three sides. Since the two legs have length $a = 3$ ft and the hypotenuse $c\approx4.242$ ft, $P=3 + 3+4.242=10.242\approx10.2$ ft.

Answer:

A. 10.2 ft