Answer:
9). 15 miles
10). 12880.8 in²
Step-by-step explanation:
9). Total distance to be covered by Kelly = Perimeter of the given triangle
= Sum of three sides of the triangle
To know the length of Laurel drive (Hypotenuse of the triangle), we will apply Pythagoras theorem in the given triangle,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
= (2.5)²+ 6²
= 6.25 + 36
Hypotenuse = [tex]\sqrt{42.25}[/tex]
= 6.5 mi.
Therefore, total distance covered by Kelly = 6.5 + 2.5 + 6
= 15 mi.
10). Amount of paper required to cover one desk of the class
= Area of the trapezoid shown in the figure
= [tex]\frac{1}{2}(b_1+b_2)h[/tex]
Here, [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel sides of the trapezoid
And 'h' is the distance between the parallel sides.
By applying Pythagoras theorem in ΔPRT,
PR² = RT² + PT²
PT = [tex]\sqrt{PR^2-RT^2}[/tex]
PT = [tex]\sqrt{(18)^2-2^2}[/tex]
= [tex]\sqrt{324-4}[/tex]
= [tex]\sqrt{320}[/tex]
= 17.89 in.
Area of the trapezoid PQRS = [tex]\frac{1}{2}(PQ+RS)(PT)[/tex]
= [tex]\frac{1}{2}(22+26)(17.89)[/tex]
= 429.36 in²
Therefore, paper required to cover 30 desks = 30 × 429.36
= 12880.8 in²
