Answer:
Q7. 11.3 inches (3 s.f.)
Q8. 96.2 ft
Q9. 36.4cm
Step-by-step explanation:
Q7. Please see attached picture for full solution.
Q8. Let the length of a side of the square be x ft.
Applying Pythagoras' Theorem,
[tex]34^{2} = {x}^{2} + {x}^{2} \\ 2 {x}^{2} = 1156 \\ {x}^{2} = 1156 \div 2 \\ {x}^{2} = 578 \\ x = \sqrt{578} \\[/tex]
Thus, the perimeter of the square is
[tex] = 4( \sqrt{578} ) \\ = 96.2 ft\: \: \: (3 \: s.f.)[/tex]
Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.
Since the perimeter of the equilateral triangle is 126cm,
length of each side= 126÷3 = 42 cm
The green line drawn in picture 3 is the altitude of the triangle.
Let the altitude of the triangle be x cm.
sin 60°= [tex] \frac{x}{42} [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{x}{42} \\ x = \frac{ \sqrt{3} }{2} \times 42 \\ x = 21 \sqrt{3} \\ x = 36.4[/tex]
(to 3 s.f.)
Therefore, the length of the altitude of the triangle is 36.4cm.
