The base of a triangle is 3 inches more than 4 times the height. If the area of the triangle is 11 square inches, find the base and height.

Answer 1

Set up system of equations:

b = 4h + 3

A = .5 * b * h = 11

Substitute b in terms of h from the first equation into the second equation and solve for h:

.5 * b * h = 11

.5 * (4h + 3) * h = 11

(4h + 3) * h = 22

4h² + 3h = 22

4h² + 3h - 22 = 0

(4h + 11) (h - 2) = 0

h = -11/4 OR h = 2

Reject the negative answer since a length cannot be negative

=> h = 2

Plug h value into the first equation to solve for b:

b = 4h + 3 = 4(2) + 3 = 11

base = b = 11

height = h = 2

Answer 2

b=3+4h

bh/2 = 11

(3+4h)h/2 =11

3h+4h^2 =22

4h^2+3h-22 = 0

(4h+11)(x-2)=0

h=2

ignore the negative height

b=3+4h = 3 + 4x2 = 11

base= 11 inches, height = 2 inches

Area = (1/2)(11x2) = 11 square inches

hb/2 = area = (1.3)(8.2)/2 = (1.3)(4.1) = 5.33