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A rectangle's base is 5 cm longer than its height. The rectangle's area is 50 cm². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is

Respuesta :

mhanifa

Answer:

  • The rectangle's height is 5 cm,
  • The rectangle's base is 10 cm.

Step-by-step explanation:

Let the dimensions be:

  • Base = b, Height = h

Given

  • b = h + 5,
  • A = 50 cm²

The area of rectangle is:

  • A = bh  
  • h(h + 5) = 50
  • h² + 5h = 50
  • h² + 5h - 50 = 0
  • h² - 5h + 10h - 50 = 0
  • h(h - 5) + 10(h - 5) = 0
  • (h - 5)(h + 10) = 0
  • h - 5 = 0 and h + 10 = 0
  • h = 5 and h = - 10

The second value of h is negative and therefore discarded.

So we get:

  • h = 5 cm,
  • b = 5 + 5 = 10 cm

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