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The are of a triangle is 25 squared

The are of a triangle is 25 squared-example-1
User Maets
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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

User Alo
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