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Linear Equations in one Variable — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSLinear Equations in one Variable4 Marks
Question
A rectangle’s length is $5 \ cm$ less than twice its width. If the length is decreased by $5 \ cm$ and width is increased by $2 \ cm$; the perimeter of the resulting rectangle will be $74 \ cm$. Find the length and width of the origi¬nal rectangle.
✓

Answer

Let width of the original rectangle $= x \ cm$ Length of the original rectangle $= (2x – 5)cm$
Now, new length of the rectangle $= 2x – 5 – 5 = (2x – 10) \ cm$
New width of the rectangle $= (x + 2) \ cm$
New perimeter $= 2[$Length+Width$] = 2[2x – 10 + x + 2] = 2[3x – 8] = (6x – 16) \ cm$
Given; new perimeter $= 74 \ cm$
$6x – 16 = 74$
$\Rightarrow 6x = 74 + 16$
$\Rightarrow 6x = 90$
$\Rightarrow x = 15$
Length of the original rectangle $= 2x – 5 = 2 \times 15 – 5 = 30 – 5 = 25 \ cm$
Width of the original rectangle$ = x = 15 \ cm$

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