Question

бічна сторона рівнобедреного трикутника дорівнює 15 см а висота проведена до основи на 6 см менша від основи знайдіть периметр цього трикутника

Answer 1

Розв'язання на фото

Відповідь:48 см

Answer 2

#### Given Information We are given the following information about the isosceles triangle: - The length of one of the equal sides is 15 cm. - The height drawn to the base is 6 cm less than the base. #### Solution To find the perimeter of the triangle, we need to determine the lengths of the other two sides. Let's assume that the length of the base of the triangle is 'b' cm. Since the height drawn to the base is 6 cm less than the base, the length of the height is 'b - 6' cm. Using the Pythagorean theorem, we can find the length of the other two sides of the triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In our case, the triangle is not a right triangle, but we can still use the Pythagorean theorem to find the lengths of the other two sides. Let's consider the right triangle formed by half of the base, the height, and the hypotenuse (one of the equal sides of the triangle). Using the Pythagorean theorem, we have: **((b/2)^2) + ((b - 6)^2) = 15^2** Simplifying the equation, we get: **(b^2)/4 + (b^2 - 12b + 36) = 225** Multiplying through by 4 to eliminate the fraction, we get: **b^2 + 4b^2 - 48b + 144 = 900** Combining like terms, we have: **5b^2 - 48b + 144 = 900** Rearranging the equation, we get: **5b^2 - 48b - 756 = 0** Now, we can solve this quadratic equation to find the value of 'b'.