Answer:
Question #5
x = 3
CE = 21
DE = 16
CD = 21
Question #6
x = 9
QR = 35
RS = 35
QS = 35
Step-by-step explanation:
Question #5
ΔCDE is an isosceles triangle which means that two of the sides are congruent. We also know that ∠D ≅ ∠E which means that C is the vertex angle. (*The vertex angle is the angle formed by the two congruent sides)
Since ∠D ≅ ∠E, we know that CD and CE are the two congruent sides of the triangle since the vertex angle is formed by the two congruent sides meaning that the two congruent sides are going to both include C as one of their ending points.
CD = 4x + 9
DE = 7x - 5
CE = 16x - 27
Since CD and CE are the two congruent sides, their measurements will also be equal. With this is mind we can set up this equation:
CE = CD
4x + 9 = 16x - 27
Solve for x.
4x + 9 = 16x - 27
9 = 12x - 27
36 = 12x
x = 3
Now that we know the value of x, we can use it to find the measurements of the triangle's sides.
CD = 4x + 9
CD = 4(3) + 9
CD = 12 + 9
CD = 21
DE = 7x - 5
DE = 7(3) - 5
DE = 21 - 5
DE = 16
CE = 16x - 27
CE = 16(3) - 27
CE = 48 - 27
CE = 21
Question #6
ΔQRS is an equilateral triangle which means that all of its sides are equal. But first, lets get our equations for each side established:
QR = 2x + 17
RS = 6x - 19
QS = 4x -1
Since all of this triangle's sides are equal, pick any side to set equal to a second side and then solve for x.
QR = RS
2x + 17 = 6x - 19
17 = 4x - 19
36 = 4x
x = 9
Now that we know the value of x, we can use it to find the measurements of the triangle's sides.
QR = 2x + 17
QR = 2(9) + 17
QR = 18 + 17
QR = 35
RS = 6x - 19
RS = 6(9) - 19
RS = 54 - 19
RS = 35
QS = 4x -1
QS = 4(9) - 1
QS = 36 - 1
QS = 35
~Hope this helps!~
