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In rectangle ABCD, AB = x, BC =x + 2, and AC = x +4. Find the value of x.

User Sam Spade
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1 Answer

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Answer:

x = 6

Explanation:

the diagonal AC divides the rectangle into 2 right triangles.

Consider the right triangle ABC with legs AB , BC and hypotenuse AC

using Pythagoras' identity in right triangle ABC

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + BC² = AC² ( substitute values )

x² + (x + 2)² = (x + 4)² ← expand factors using FOIL

x² + x² + 4x + 4 = x² + 8x + 16

2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

however , x > 0 , then x = 6

User Manubkk
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