In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 . What is BD ?
2 answers:
Refer to the diagram shown below.
BE = 2x² - x
DE = x² + 6
The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.
When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20
When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30
Answer: Either 20 or 30.
BE = 2x² - x
DE = x² + 6
The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.
When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20
When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30
Answer: Either 20 or 30.
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In this question , we have to find the value of tan 30 and we need to write the answer in simplified form .
Substituting the values of sin (30) and cos(30, we will get
Multiplying both numerator and denominator by 2, we will get
TO simplify it, we need to multiply both numerator and denominator by square root 3.