Length and width of the rectangle are 4 cm and 2.5 cm respectively.
Given in the picture,
- A rectangle with the area of 10 cm².
- Expressions representing the lengths of the rectangle as
(4x + 2) cm and (10x - 1) cm
By the property of a rectangle, measure of opposite sides of a rectangle are always equal,
(4x + 2) = (10x - 1)
(4x + 2) - 4x = (10x - 1) - 4x
2 = 6x - 1
2 + 1 = (6x - 1) + 1
3 = 6x
[tex]x=\frac{3}{6}=\frac{1}{2}[/tex]
Now we can get the length of the given rectangle by substituting the value of 'x' in (10x - 1) or (4x + 2).
(10x - 1) = [tex]\frac{10}{2}-1[/tex]
= 4 cm
Since, area of a rectangle is given by the expression,
Area = Length × width
By substituting the values in the expression,
10 = 4 × width
Width = [tex]\frac{10}{4}[/tex]
= 2.5 cm
Therefore, length and width of the rectangle are 4 cm and 2.5 cm respectively.
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