Respuesta :
The length and the width of the rectangle are 2 inches and 13 inches respectively.
What is a rectangle?
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Let the width of the rectangle be represented by x.
Given the length of a rectangular poster is 7 more inches than three times its width. Therefore, the length can be written as,
Length = (3 × width)+7 more inches = 3x+7
Also, given the area of the poster is 26 sq. inches, therefore, the area of will be,
26 = x × (3x+7)
26 = 3x² + 7x
3x² + 7x - 26 = 0
[tex]x = \dfrac{-(7)\pm\sqrt{(7)^2-4(3)(-26)}}{2(3)}\\\\x = 2, -4.333[/tex]
Since the width can not be negative, therefore, the width of the rectangle is 2. The dimensions of the rectangle are,
Width = x = 2 inches
Length = 3x + 7 = 13 inches
Hence, the length and the width of the rectangle are 2 inches and 13 inches respectively.
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