Answer:
NF = 25
Step-by-step explanation:
Since ∆NKF ~ ∆LZF, the ratio of their corresponding side lengths would also be the same.
This means that:
KF/ZF = NF/LF
KF = x + 3
ZF = 4
NF = 15 + x + 3 = x + 18
LF = x + 3
Plug in the values into the equation
(x + 3)/4 = (x + 18)/(x + 3)
Cross multiply
(x + 3)(x + 3) = (x + 18)(4)
x² + 3x + 3x + 9 = 4x + 72
x² + 6x + 9 = 4x + 72
x² + 6x + 9 - 4x - 72 = 0
x² + 2x - 63 = 0
Factorize to find x
x² + 9x - 7x - 63 = 0
x(x + 9) -7(x + 9) = 0
(x + 9)(x - 7) = 0
x + 9 = 0 or x - 7 = 0
x = -9 or x = 7
We'd use the positive value of x, which is 7.
Therefore, x = 7.
✅NF = 15 + (x + 3)
Plug in the value of x
NF = 15 + (7 + 3) = 15 + 10
NF = 25
Answer:
Height= 4m (nearest meter)
Step-by-step explanation:
Diameter= 2(radius)
Given that the diameter is 12m,
radius of cone
= 12 ÷2
= 6m
Let the height of the cone be h meters.
h= 4.0054 (5 s.f.)
Thus, the height of the cone is 4m. (nearest meter)
L = 2w + 6
p = 144
144 = 2w + 2(2w + 6)
144 = 2w + 4w + 12
132 = 6w
w = 22
l = 2(22) + 6
l = 50
The length is 50 feet and the width is 22 feet.
Answer:
Step-by-step explanation:
9. D
10.D
11.E
12.D
