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liq [111]
3 years ago
7

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find the length of AC.

Mathematics
1 answer:
Oxana [17]3 years ago
8 0

Answer:

AC=16 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.  It was given that diagonals AC and BD intersect at point E.

This implies that: AE=CE.

We substitute the expression for x, we get:

11x-3=12-4x.

Group similar terms to get:

11x+4x=12+3.

15x=15.

x=1

AC = 2(12-4x)

AC=2(12-4(1))

AC=2(8)

AC=16

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Triangle CDE is an isosceles triangle with angle d congruent to angle E if CD= 4x+9, DE= 7x-5, CE= 16x-27, find x and the measur
Montano1993 [528]
ANSWER

x = 3
CD= 21 \: units
DE= 16 \: units

CE= 21 \: units



EXPLANATION

It was given that ∆CDE is an isosceles triangle.

The length of the sides are given in terms of x as follows.

CD=4x+9


DE=7x-5


CE=16x-27



It was also given that, angle D is congruent to angle E.


This implies that, side CD and CE are equal.


Thus,

|CD|  =  |CE|
In terms of x, we have;

4x + 9 = 16x - 27


We group like terms to get,

16x - 4x = 9 + 27

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Divide both sides by 12 to get,

x =  \frac{36}{12}

\therefore \: x = 3


The length of the sides are;

CD=4(3)+9 = 21 \: units

DE=7(3)-5 = 16 \: units


CE=16(3)-27 = 21 \: units
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3 years ago
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The three sides of a triangle are n, 3n + 5, and 4n − 9. If the perimeter of the triangle is 68 feet, what is the length of each
MissTica
4n - 9 + 3n + 5 + n = 68

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division property of equality

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SIDES:

n = 9

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[ 4(9) - 9 = 27 ]
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3 years ago
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