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Right triangle trigonometry: advanced ep 19 10 ft A room has the shape of a rectangle with a right triangle taken from one of its corners as shown. The rectangle has a length of 22 feet ( ft ) and a width of 19 ft . Both sides next to the removed corner have a length of 10 ft . What is the perimeter of the room in feet? 70 qquad

Right triangle trigonometry: advanced\newlineep 1919\newline1010 ft\newlineA room has the shape of a rectangle with a right triangle taken from one of its corners as shown. The rectangle has a length of 2222 feet ( ft ) and a width of 1919 ft . Both sides next to the removed corner have a length of 1010 ft . What is the perimeter of the room in feet?\newline7070 \qquad

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Q. Right triangle trigonometry: advanced\newlineep 1919\newline1010 ft\newlineA room has the shape of a rectangle with a right triangle taken from one of its corners as shown. The rectangle has a length of 2222 feet ( ft ) and a width of 1919 ft . Both sides next to the removed corner have a length of 1010 ft . What is the perimeter of the room in feet?\newline7070 \qquad
  1. Find Hypotenuse Length: First, find the length of the hypotenuse of the right triangle using the Pythagorean theorem.
    a=10 fta = 10 \text{ ft}, b=10 ftb = 10 \text{ ft}
    c2=a2+b2c^2 = a^2 + b^2
    c2=102+102c^2 = 10^2 + 10^2
    c2=100+100c^2 = 100 + 100
    c2=200c^2 = 200
    c=200c = \sqrt{200}
    c=102 ftc = 10\sqrt{2} \text{ ft}
  2. Calculate Perimeter: Calculate the perimeter of the room by adding the lengths of all sides. Perimeter = 22 ft (length)+19 ft (width)+22 ft (length)+19 ft (width)−10 ft (side of triangle)−10 ft (side of triangle)+102 ft (hypotenuse)22 \text{ ft (length)} + 19 \text{ ft (width)} + 22 \text{ ft (length)} + 19 \text{ ft (width)} - 10 \text{ ft (side of triangle)} - 10 \text{ ft (side of triangle)} + 10\sqrt{2} \text{ ft (hypotenuse)} Perimeter = 22+19+22+19−10−10+10222 + 19 + 22 + 19 - 10 - 10 + 10\sqrt{2} Perimeter = 62+102 ft62 + 10\sqrt{2} \text{ ft}
  3. Approximate Hypotenuse Value: Approximate the value of 10210\sqrt{2} to simplify the final answer. 102≈10×1.414≈14.1410\sqrt{2} \approx 10 \times 1.414 \approx 14.14 ft Perimeter ≈62+14.14\approx 62 + 14.14 Perimeter ≈76.14\approx 76.14 ft

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