Question - Solving Right-Angled Triangle Problems with the Pythagorean Theorem
Solution:
The image shows two separate mathematical problems involving right-angled triangles, one labeled as question 4 and the other as question 5. Both problems are about finding the length of the missing side of the triangle, which is a classic Pythagorean theorem problem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.For question 4, the sides of the triangle are given as 3 (one leg) and 4 (the other leg), and we are to find the hypotenuse. By applying the Pythagorean theorem (a^2 + b^2 = c^2), where 'c' is the hypotenuse and 'a' and 'b' are the other sides, we can solve the triangle:3^2 + 4^2 = c^29 + 16 = c^225 = c^2c = √25c = 5So, the length of the hypotenuse is 5 and the correct answer is not shown as marked in the image.For question 5, the sides of the triangle are given as 7 (one leg) and 24 (the other leg), and we are to find the hypotenuse. We apply the Pythagorean theorem again:7^2 + 24^2 = c^249 + 576 = c^2625 = c^2c = √625c = 25The length of the hypotenuse for question 5 is therefore 25, which corresponds with answer choice B.To summarize:- Question 4: The hypotenuse = 5 (not in the choices)- Question 5: The hypotenuse = 25 (choice B)
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