Question

The height of a triangle is 7 ft more than its base. If the area of the triangle is 30 ft2, what is the length of the base?

2 ft


5 ft


9 ft


12 ft

Answer 1

see below

Step-by-step explanation: 5 27 7 16

area = 1/2 bh

height of a triangle is 7 ft more than its base

base = b

height = b + 7

area = 30

area = 1/2 b(h)

30 = 1/2 b(b + 7)

30 = 0.5(b²+ 7b)

30 = 1/2 b²+ 3.5b solve for b

1/2 b²+ 3.5b = 30

1/2 b²+ 3.5b - 30 = 0

b²+ 7b - 60 = 0 factor

(b +12)(b - 5) = 0 when b = -12 or 5 base length can't be negative

b = base = 5

area = 1/2 bh 1/2×2(9) = 9

area = 1/2 bh 1/2×5(12) = 60

area = 1/2 bh 1/2×9(16) = 56

area = 1/2 bh 1/2×12(19) = 114