The base of the triangular prism is a right-angled triangle with legs 3 and 4, the height of the prism
| August 14, 2021 | education
The base of the triangular prism is a right-angled triangle with legs 3 and 4, the height of the prism is 12. Find the largest of the diagonals of the side faces of the prism.
Since at the base of the prism lies a right-angled triangle, then by the Pythagorean theorem we determine the length of the hypotenuse AC.
AC ^ 2 = AB ^ 2 + BC ^ 2 = 9 + 16 = 25.
AC = 5 cm.
The side faces of a straight prism are rectangles with the same heights. AA1 = BB1 = CC1 = 12 cm. Then the largest of the diagonals of the side face is the diagonal of the rectangle and the large base.
The side face of АА1С1С is large, then the diagonal АС1 is large.
By the Pythagorean theorem, AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 25 + 144 = 169.
AC1 = 13 cm.
Answer: The large diagonal is 13 cm.
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