For a square ABCD, the side BC = 13 units. A is at (.x, 8) and B is at (-7,3) Also, x > 0. Find.x​

Question

For a square ABCD, the side BC = 13 units.
A is at (.x, 8) and B is at (-7,3)
Also, x > 0.
Find.x​

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Latifah 4 years 2021-08-10T10:04:31+00:00 1 Answers 40 views 0

Answers ( )

  1. ngochoa
    0
    2021-08-10T10:05:31+00:00
    Reply

    Answer:

    x = 5

    Step-by-step explanation:

    Since all the sides of a square is equal then AB = BC

    Given BC = 13 units and A is at (.x, 8) and B is at (-7,3)

    To get AB, we will find the distance between the two coordinates as shown;

    AB = √(x₂-x₁)²+(y₂-y₁)²

    AB = √(-7-x)²+(3-8)²

    Since AB = BC, then AB = 13

    13 = √(-7-x)²+(3-8)²

    square both sides

    13² = (√(-7-x)²+(3-8)²)²

    169 = (-7-x)²+(3-8)²

    169 = 49+14x+x²+(-5)²

    169 = 49+14x+x²+25

    169 = x²+14x+74

    x²+14x+74-169 = 0

    x²+14x+74-169 = 0

    x²+14x-95= 0

    x²+19x-5x-95= 0

    x(x+19)-5(x+19) = 0

    x-5 = 0 and (x+19) = 0

    x = 5 and x = -19

    Since x> 0, hence the value of x is 5

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