The length of the side AB is 14 units.
The value of x is 17 and the value of y is 25.3
Explanation:
3) It is given that, the triangles ABC and DEF are similar.
The properties of similar triangles are given as :
- The corresponding angles are same.
- The corresponding sides are all in the same proportion.
Therefore, the sides AB and ED are corresponding sides and are in same proportion.
⇒ AB = 6y - 4
⇒ ED = 4y + 2
To solve for y value :
⇒ 6y - 4 = 4y+2
⇒ 6y - 4y = 2 + 4
⇒ 2y = 6
⇒ y = 6 / 2
⇒ y = 3
To find the side AB :
Substitute y = 3 in AB,
⇒ 6(3) - 4
⇒ 18 - 4
⇒ 14
∴ The length of the side AB is 14 units.
4) To find x and y values :
Since, the two triangles are similar, the angle D is equal to angle A.
⇒ ∠D = 5x + 2
⇒ ∠A = 87
To solve for x value :
⇒ 5x + 2 = 87
⇒ 5x = 87 - 2
⇒ 5x = 85
⇒ x = 85 / 5
⇒ x = 17
∴ The value of x is 17.
Again, the angles C and F are equal. But the angle F is not given.
To find angle F :
Sum of all three angles of triangle = 180 degree
42 + (5x+2) + ∠F = 180
Substitute x = 12,
42 + (5(12)+2) + ∠F = 180
42 + 62 + ∠F = 180
∠F = 180 - 104
∠F = 76°
Now, to solve for y value :
⇒ ∠F = 76 and ∠C = 3y are equal
⇒ 3y = 76
⇒ y = 76/3
⇒ y = 25.3
∴ The value of y is 25.3