Janelle S. answered • 09/24/20

Penn State Grad for ME, Math & Test Prep Tutoring (10+ yrs experience)

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

4h^{2} + 3h = 22

4h^{2} + 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