Answer: x = 12
Step-by-step explanation:
We can see two triangles rectangles, we will use the angle S to solve this, as this angle is common to both triangles.
We know that:
cos(S) = adj cathetus/hipotenuse.
Then we have, for the triangle SRT.
Cos(S) = 9/SR.
for the big triangle, SQR, we have:
Cos(S) = SR/(9 + 16)
now we can find the quotient of those two equations and get:
cos(S)/cos(S) = 9/Sr*(9+16)/SR
SR^2 = 9*(25)
SR = 15.
Now with this side we can find the value of x.
We can use the Pythagorean theorem in the triangle SRT, where the sum of the squared cathetus is equal to the hypotenuse:
9^2 + x^2 = 15^2
x = √(15^2 - 9^2) = 12
Let x = your number.
x^2 - 21 = 4x. Subtract 4x from both sides.
x^2 - 4x - 21 = 0. Factor.
(x - 7) (x + 3) = 0. Set each term to 0.
x + 3 = 0. Subtract 3 from both sides.
x = -3. This is the negative solution.
Set the other term equal to zero.
x - 7 = 0. Add 7 to each side.
x = 7. This is the positive solution.
Answer:
- (a) 104 = 4(12+x)
- (b) x = 14
Step-by-step explanation:
(a) The new side length of Ben's garden is (12+x), since x is the amount of increase above the existing 12 ft side length.
The perimeter is the sum of the lengths of the four equal sides, so is ...
perimeter = 4 × side length
104 = 4(12+x)
(b) We can solve this by dividing by 4, then subtracting 12.
26 = 12 +x . . . . . divide the above equation by 4
14 = x . . . . . . . . . subtract 12
The solution is x = 14.
True
<span>Vertical angles are opposite angles with the same vertex </span>
