Question

Основание равнобедренной трапеции равны 9 и 51, боковая сторона 75, найти длину диагонали

Answer 1

Обозначим трапецию АВСД, проведём диагональ АС.
Из вершин В и С опустим высоты на основание, обозначим ВК -одна высота,
СН - другая высота.
АК = НД = (АД - ВС) : 2 = (51 - 9) : 2 = 21 (т.к. трапеция равнобедренная)
ВК^2 = СН^2 = CД^2 - HД^2 = 75^2 - 21^2 = 5625 - 441 = 5184 (по т. Пифагора)
ВК = СН = 72
AН = 51-21 = 30
АС ^2 = CH^2 + AH^2 (по теореме Пифагора)
АС^2 = 72^2 +30^2 = 5184 + 900 = 6084
AC = 78
Ответ: диагональ АС = 78

Answer 2

Finding the Length of the Diagonal of an Isosceles Trapezoid

To find the length of the diagonal of an isosceles trapezoid, we need to use the given information about the bases and the side length. Let's break down the problem step by step.

Given information: - The bases of the trapezoid are 9 and 51. - The side length of the trapezoid is 75.

To find the length of the diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 other two sides.

In this case, we can consider the diagonal as the hypotenuse of a right triangle, with the bases and the side length as the other two sides.

Let's denote the length of the diagonal as d.

Using the Pythagorean theorem, we can write the equation:

d^2 = (9 + 51)^2 + 75^2

Simplifying the equation:

d^2 = 60^2 + 75^2

d^2 = 3600 + 5625

d^2 = 9225

Taking the square root of both sides to find the length of the diagonal:

d = √9225

d = 95

Therefore, the length of the diagonal of the isosceles trapezoid is 95 units.