L=2W+2
W=(L-2)/2
A=LW, using W from above makes this
A=L(L-2)/2
2A=L^2-2L
L^2-2L-2A=0, given A=84
L^2-2L-168=0
(L-14)(L+12)=0, since L>0
L=14
The length of the rug is 14 ft
(W=(L-2)/2=6 ft)
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
5x + 7 + 4x + 2 + 90 = 180 , that is
9x + 99 = 180 ( subtract 99 from both sides )
9x = 81 ( divide both sides by 9 )
x = 9
Then
∠ ACB = 4x + 2 = 4(9) + 2 = 36 + 2 = 38°
∠ BAC = 5x + 7 = 5(9) + 7 = 45 + 7 = 52°
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Since the triangles are congruent then corresponding angles are congruent , so
∠ B = ∠ E
6x + 10 = 70 ( subtract 10 from both sides )
6x = 60 ( divide both sides by 6 )
x = 10
Answer:
The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees
Step-by-step explanation:
4a) Given the following
Opposite side = 38cm (side facing the given angle)
Required
Adjacent and hypotenuse side
According to SOH CAH TOA
Next is to get the adjacent
Next is to get the missing
Since sum of angle in the triangle is 180degrees
32 + 90 + x = 180
122 + x = 180
x = 180 - 122
x = 58degrees
1/2 (6x - 10) + 10 = 5x - 13
(6x/2) - (10/2) + 10 = 5x - 13
3x - 5 + 10 = 5x - 13
3x - 5x = -13 + 5 - 10
-2x = -18
x = -18 / -2
x = 9
D.) x = 9
This is not going to be a hole number, it's about 4.0666
