Answer:
Explanation:
area of the triangle is, 1/2 * b * h
according to the question,
base, b = x
height, h = (2x + 1)
area of the triangle is, 25cm²
by substituting the values in the formula,
25 = 1/2 * (2x + 1) * x
25 * 2 = (2x + 1) * x
50 = 2x² + x
2x² + x - 50 = 0
a) thus, the equation is reduced to 2x² + x - 50 = 0
b)
steps to complete the square are as follows:
2x² + x - 50 = 0
dividing the whole equation by (2)
x² + x/2 - 50/2 = 0
x² + x/2 - 25 = 0
taking the half of the middle, x term
in this case it is, 1/4
adding the square of the middle half term to both sides, i,e, adding 1/16 to both sides,
x² + 1/2x + 1/16 = 25 + 1/16
(x + 1/4)² = 400 + 1 / 16
(x + 1/4)² = 401/16
x + 1/4 = √401/16
x = √401/4 - 1/4
as √401 is approximately 20
= 20 - 1 / 4 = 19/4
length of the base of triangle, 2x + 1
= 2(19/4) + 1
= 19/2 + 1 = 19 + 2 / 2
= 21/2 = 10.5