The height of a triangle is 4 cm more than twice its base. The area of the triangle is 168 cm^2. What is the length of the base of the triangle? a) 12 cm
b) 6 cm
c) 7 cm
d) 14 cm

12cm

Step-by-step explanation:

h = 2b + 4

Area = 168 cm²

b = ?

Area = b*h / 2

168 = b (2b + 4) / 2

168 = 2b² + 4b/ 2

168 = b² + 2b

b² + 2b - 168 = 0

(b + 14) (b - 12) = 0

b = -14

b = 12

The base of a triangle cannot be -ve. So b = 12cm

angles 1 and 3 are vertical angles, meaning that they are equal to each other. to solve this you may set angle 1 and 3 equal to each other and just solve for x like

110 = 2x + 10

100 = 2x

50 = x

check:

110 = 2* 50 + 10

110 = 100 + 10

110 = 110

hope this !

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step-by-step explanation: