We know that the law of sines states that:
For simplicity, let:
In triangle A1BC this leads to:
Therefore:
Now, triangle A2BC is isosceles which means that both the base angles are equal, since angle CA1B and A2A1B are supplementary we have:
Supplementary angels complementary angels and congruent angles
X - 4 = -4 -4
Combine the two -4.
X - 4 = -8
Add 4 on both sides to isolate the x and get your answer.
X = -4
2 - 3x = -x - 8
Subtract the 2 on both sides.
-3x = -x - 10
Add the x on both sides.
-2x = -10
Divide by -2 on both sides to isolate the x and get your answer.
x = 5
Answer:
The length of the garden=14 feet
Step-by-step explanation:
<em>Step 1: Determine the dimensions of the garden</em>
length of the garden=x feet
width of the garden=(x-4) feet
<em>Step 2: Determine the area of the garden</em>
Area of the garden=length×width
where;
area=140
length=x
width=x-4
replacing'
x(x-4)=140
x²-4x-140=0, solve the quadratic equation;
x={-b±√(b²-4ac)}/2a
x={4±√4²-4×1×-140}/2×1
x={4±√(16+560)}/2
x={4±√576}/2
x=(4±24)/2
x=(4+24)/2=14, or (4-24)/2=-10, take x=14
The length=14 feet, width=(14-4)=10 feet
The length of the garden=14 feet
