Question

I need help with these three problems please​

Answer 1

7) 8sqrt(2) in

8) 68sqrt(2) ft

9) 21sqrt(3) cm

Explanation:

7) sqrt(8² + 8²) = 8sqrt(2) in

sqrt is square root

8) sqrt(x² + x²) = 34

2x² = 34²

x = 17sqrt(2)

Perimeter = 4x = 68sqrt(2) ft

9) 3s = 126

s = 42

Altitude² + 21² = 42²

Altitude² = 1323

Altitude = 21sqrt(3) cm

Answer 2

Q7. 11.3 inches (3 s.f.)

Q8. 96.2 ft

Q9. 36.4cm

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,

`34^(2) = {x}^(2) + {x}^(2) \\ 2 {x}^(2) = 1156 \\ {x}^(2) = 1156 / 2 \\ {x}^(2) = 578 \\ x = √(578) \\`

Thus, the perimeter of the square is

`= 4( √(578) ) \\ = 96.2 ft\: \: \: (3 \: s.f.)`

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°=
`(x)/(42)`

`( √(3) )/(2) = (x)/(42) \\ x = ( √(3) )/(2) * 42 \\ x = 21 √(3) \\ x = 36.4`

(to 3 s.f.)

Therefore, the length of the altitude of the triangle is 36.4cm.