This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the area of the isosceles triangle, we first need to determine its height. We can do this by drawing an altitude from the apex to the base, which will divide the isosceles triangle into two congruent right-angled triangles. Step 1: Identify the base and equal sides. The base of the triangle is |PQ| = 10 m. The equal sides are |PR| = 13 m and |QR| = 13 m. Step 2: Find the height of the triangle. When an altitude is drawn from the apex to the base of an isosceles triangle, it bisects the base. So, half of the base is 10 m2 = 5 m. Now, we have a right-angled triangle with a hypotenuse of 13 m and one leg of 5 m. Let h be the height (the other leg). Using the Pythagorean theorem (a^2 + b^2 = c^2): h^2 + (5 m)^2 = (13 m)^2 h^2 + 25 m^2 = 169 m^2 h^2 = 169 m^2 - 25 m^2 h^2 = 144 m^2 h = sqrt(144 m)^2 h = 12 m Step 3: Calculate the area of the triangle. The formula for the area of a triangle is Area = (1)/(2) × base × height. Area = (1)/(2) × 10 m × 12 m Area = 5 m × 12 m Area = 60 m^2 The area of the triangle is 60 m^2. Send me the next one 📸