Find three consecutive even numbers whose sum is 96. 6. The length of a rectangle exceeds twice its width by 3.Find the length and width of the rectangle if its perimeter is 246m.
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Step-by-step explanation:
★ Question Ist :
Let,
The consecutive even numbers :
- x
- x + 2
- x + 4
According to the question:
⇒ x + (x + 2) + (x + 4) = 96
⇒ 3x + 6 = 96
⇒ 3x = 96 - 6
⇒ 3x = 90
⇒ x = 90 / 3
⇒ x = 30
★ x + 2 :
⇒ 30 + 2
⇒ 32
★ x + 4 :
⇒ 30 + 4
⇒ 34
Therefore,
The consecutive even numbers are 30, 32, 34
____________________________
Question II nd :
Let,
Width = x
Length = 2x + 3
Perimeter = 246 m
⇒ 2 (length + width ) = perimeter of rectangle
⇒ 2 ( 2x + 3 + x) = 246
⇒ 2 (3x + 3) = 246
⇒ 6x + 6 = 246
⇒ 6x = 246 - 6
⇒ 6x = 240
⇒ x = 240 / 6
⇒ x = 40
★ Length = 2x + 3 :
⇒ 2 (40) + 3
⇒ 2 × 40 + 3
⇒ 80 + 3
⇒ 83
Therefore,
The length is 83 m
The width is 40 m
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