Answer:
Height of the triangle is 6 feet and base of the triangle is 4 feet.
Step-by-step explanation:
Area of a triangle is given by the formula,
Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
Let the height of triangle = h feet
Since, base of the triangle is 2 feet less than its height then base of the triangle = (h - 2) feet
Area = [tex]\frac{1}{2}h(h-2)[/tex]
[tex]12=\frac{1}{2}h(h-2)[/tex]
h² - 2h - 24 = 0
h² - 6h + 4h - 24 = 0
h(h - 6) + 4(h - 6) = 0
(h + 4)(h - 6) = 0
h = -4, 6 feet
Since height of the triangle can not be negative, therefore, height of the triangle = 6 feet.
And base of the triangle = (h - 2) = 6 - 2
= 4 feet
Height of the triangle is 6 feet and base of the triangle is 4 feet.
