Saved Bookmarks
| 1. |
The side of a square is 9cm.find the ratio of diagonal of a square to its side |
|
Answer» Step-by-step explanation: The diagonal and two adjacent sides of the square form an isosceles right triangle. Recall from trigonometry that the reference isosceles right triangle has HYPOTENUSE equal to 1 and its two LEGS each have length 2√ 2. Since all plane isosceles right triangles are similar, MULTIPLY the LENGTHS of the sides and the length of the hypotenuse of the reference triangle by 9. The RESULTING triangle has a diagonal of length 9. ∴ the length of a side of the given square is 92–√2 cm. 2.) Another way is to let s be the length of a side of the square. Again, the 9-cm diagonal and two adjacent sides form an isosceles right triangle. By the Pythagorean theorem s2+s2=(9 cm)2 ⟹2s2=81 cm2 ⟹s2=812 cm2 ⟹s2−−√=812 cm2−−−−−−√ ⟹s=81−−√2–√cm2−−−√ = 92–√ cm. |
|