The two sides of a rectangle are x and x + 1. If the length of the diagonal of the rectangle is 5 cm, then what is the area of the rectangle?



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Answer:

12 cm2

Step by Step Explanation:
  1. Given the two sides and diagonal of the rectangle ABCD are x, x + 1 and 5 respectively, as shown below:

    Let A be the area of the the rectangle ABCD.
    Area of the rectangle ABCD (A)
    = (x)(x + 1)
    = x2 + x
  2. In triangle ABC, by using Pythagoras Theorem we get,
    (x)2 + (x + 1)2 = (5)2
    ⇒ x2 + x2 + 2x + 1 = 25
    ⇒ 2x2 + 2x + 1 = 25
    ⇒ 2x2 + 2x + 1 - 25 = 0
    ⇒ 2x2 + 2x - 24 = 0
    ⇒ 2(x2 + x - 12) = 0
    ⇒ x2 + x - 12 = 0
    ⇒ 1x2 + 4x - 3x -12 = 0
    ⇒ x(1x + 4) - 3(1x + 4) = 0
    ⇒ (1x + 4)(x - 3) = 0
    either, 1x + 4 = 0 | or, x - 3 = 0
    ⇒ x = -4/1 | ⇒ x = 3

    The value of x can not be negative. So the value of x is 3.
  3. Now, the area of the rectangle ABCD = x2 + x
    = (3)2 + (3)
    = 12
  4. Therefore, the area of the rectangle is 12.

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