Question

select the correct answer.
a triangular tabletop has the given dimensions. vinyl is placed around the outer edges of the tabletop.
image of a right isosceles triangle with one leg 3 ft, base angles 45° each
what is the approximate length of vinyl needed for the outer edges of the tabletop?
a. 11.2 ft
b. 9 ft
c. 10.2 ft
d. 14.2 ft

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles \(45^{\circ}\), one right angle). So the two legs are equal. Given one leg is \(3\) ft, the other leg is also \(3\) ft.

Step2: Calculate Hypotenuse

Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = b=3\) ft. So \(c=\sqrt{3^{2}+3^{2}}=\sqrt{9 + 9}=\sqrt{18}\approx4.2\) ft.

Step3: Calculate Perimeter

Perimeter \(P=a + b + c\), where \(a = 3\) ft, \(b = 3\) ft, \(c\approx4.2\) ft. So \(P=3 + 3+4.2 = 10.2\) ft.

Answer:

C. 10.2 ft