Question

A triangle has a base of 14 centimeters and a height of ( 3x - 4 ) centimeters . The area of the triangle is greater than 56 centimeters . Solve the inequality 1/2 (14) ( 3x - 4 ) > 56 to find the possible values of x???

show your work please

Answer 1

1/2 (14) ( 3x - 4 ) > 56

14/2 (3x-4) > 56

7 (3x-4) > 56

21x - 28 > 56

21x > 56+28

21x > 84

x < 4

Answer 2

• x > 4 or x = (4, + oo)

Explanation:

The area of the triangle is

• A = 1/2bh

Given

• b = 14 cm
• h = 3x - 4

Then

• A = 1/2*14(3x - 4) = 7(3x - 4) = 21x - 28

If A > 56, then solving inequation:

• 21x - 28 > 56
• 21x > 56 + 28
• 21x > 84
• x > 84/21
• x > 4 or x = (4, + oo)