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In rhombus CATS, CA= 6x-30. AT= 2x+30 find the perimeter? I need help ASAP PLEASE

Sagot :

LadyStrange

Length of CA = 6x - 30

Length of AT = 2x + 30

We know that all sides of a rhombus are congruent.

Which means :

[tex] = 6x - 30 = 2x + 30[/tex]

[tex] = 6x - 30 - 2x = 30[/tex]

[tex] = 4x - 30 = 30[/tex]

[tex] = 4x = 30 + 30[/tex]

[tex] = 4x = 60[/tex]

[tex] = x = \frac{60}{4} [/tex]

[tex] = x = 15[/tex]

Thus, the value of x = 15

Then :

Measure of CA :

[tex] = 6x - 30[/tex]

[tex] = 6 \times 15 - 30[/tex]

[tex] = 90 - 30[/tex]

[tex] = 60[/tex]

Thus, measure of CA = 60

Measure of AT :

[tex] = 2x + 30[/tex]

[tex] = 2 \times 15 + 30[/tex]

[tex] = 30 + 30[/tex]

[tex] = 60[/tex]

Thus, measure of AT = 60

Perimefer of rhombus CAT :

[tex] = 4 \times side[/tex]

[tex] = 4 \times 60[/tex]

[tex] = \color{plum}240[/tex]

Therefore, the perimeter of rhombus CAT = 240

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