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 = ![\sqrt{42.25}](https://tex.z-dn.net/?f=%5Csqrt%7B42.25%7D)
= 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
= ![\frac{1}{2}(b_1+b_2)h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28b_1%2Bb_2%29h)
Here,
and
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 = ![\sqrt{PR^2-RT^2}](https://tex.z-dn.net/?f=%5Csqrt%7BPR%5E2-RT%5E2%7D)
PT = ![\sqrt{(18)^2-2^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%2818%29%5E2-2%5E2%7D)
= ![\sqrt{324-4}](https://tex.z-dn.net/?f=%5Csqrt%7B324-4%7D)
= ![\sqrt{320}](https://tex.z-dn.net/?f=%5Csqrt%7B320%7D)
= 17.89 in.
Area of the trapezoid PQRS = ![\frac{1}{2}(PQ+RS)(PT)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28PQ%2BRS%29%28PT%29)
= ![\frac{1}{2}(22+26)(17.89)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2822%2B26%29%2817.89%29)
= 429.36 in²
Therefore, paper required to cover 30 desks = 30 × 429.36
= 12880.8 in²