The quadrilateral ABCD has area of 58 in2 and diagonal AC = 14.5 in. Find the length of diagonal BD if AC ⊥ BD.
hi the answer is 8 because 58 = 1/2(14.5x) and x = 8
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Thanks for that answer! It was so helpful!
To find the length of diagonal BD, we can make use of the fact that the area of a quadrilateral is equal to half the product of the lengths of its diagonals when they are perpendicular to each other.
Let's denote the length of diagonal BD as x.
We know that the area of quadrilateral ABCD is 58 in². Therefore, we have:
Area = (1/2) * AC * BD
Substituting the given values, we have:
58 = (1/2) * 14.5 * x
To solve for x, we can rearrange the equation by multiplying both sides by 2 and dividing by 14.5:
2 * 58 = 14.5 * x
116 = 14.5 * x
Now, to find x, we can divide both sides of the equation by 14.5:
x = 116 / 14.5
Simplifying this gives us:
x = 8
Therefore, the length of diagonal BD is 8 inches.
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harder
not a good answer
are u kidding me
If the diagonals AC ⊥ BD then the figure is a rhombus. Since the area of a rhombus is the one-half product of the diagonals,
(29/2)*BD/2 = 58
Not so hard now, eh?