Li Wei usually gets to work by walking 1.3 miles north on 12^("th ") Street and then turning right 90^(@) and walking east on Azalia Street for 3.3 miles. His friend mentions that Li Wei could take Washington Street instead, which goes directly from his apartment to his workplace, in a straight line. Approximately how much shorter, in miles, is this route compared to Li Wei's usual walking route? (Round your answer to the nearest tenth of a mile.)

Question

Li Wei usually gets to work by walking 1.3 miles north on  12^("th ") Street and then turning right  90^(@) and walking east on Azalia Street for 3.3 miles. His friend mentions that Li Wei could take Washington Street instead, which goes directly from his apartment to his workplace, in a straight line. Approximately how much shorter, in miles, is this route compared to  Li Wei's usual walking route? (Round your answer to the nearest tenth of a mile.)

Bytelearn · Accepted Answer

Identify the legs: Identify the legs of the right triangle formed by Li Wei's usual route. Li Wei walks 1.3 miles north and then 3.3 miles east, forming a right triangle with these two distances as the legs.Use Pythagorean Theorem: Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance of the direct route on Washington Street. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). a^2 + b^2 = c^2 1.3^2 + 3.3^2 = c^2Calculate squares of legs: Calculate the squares of the legs of the triangle. 1.3^2 = 1.69 3.3^2 = 10.89Add squares for hypotenuse: Add the squares of the legs to find the square of the hypotenuse. 1.69 + 10.89 = 12.58Find length of hypotenuse: Take the square root of the sum to find the length of the hypotenuse. sqrt(12.58) ≈ 3.55 milesCalculate difference in distance: Calculate the difference in distance between Li Wei's usual route and the direct route on Washington Street. Li Wei's usual route is 1.3 miles + 3.3 miles = 4.6 miles. The direct route is approximately 3.55 miles. Difference = 4.6 miles - 3.55 miles = 1.05 milesRound difference to nearest tenth: Round the difference to the nearest tenth of a mile. Rounded difference = 1.1 miles

Full solution

More problems from Pythagorean Theorem and its converse

Related topics