In the square ABCD, AE = 3x + 5 and BD = 10x + 2. What is the length of line AC?

Mathematics

1 answer:

zubka84 [21]3 years ago

6 0

BD = 2 AE
10 x + 2 = 2 * ( 3 x + 5 )
10 x + 2 = 6 x + 10
10 x - 6 x = 10 - 2
4 x = 8
x = 8 : 4
x = 2
And the line AC is equal to BD.
AC = 10 * 2 + 2 = 20 + 2 = 22
Answer:
3. 22

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Step-by-step explanation:

Step 1:

First, we plot the coordinates of both triangles.

The coordinates of the triangle $A^{1} B^{1} C^{1}$ are as follows;

$A^{1}$ = (2, 3), $B^{1}$ = (2, 1), and $C^{1}$ = (3, 1).

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A = (4, 9), B = (4, 3), and C = (7, 3).

Step 2;

Next, we need to find the distances between at least two coordinates for both triangles.

The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.

The distance of $A^{1} B^{1} = 3-1=2$ , the distance of $B^{1} C^{1} = 3-2=1$ .