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Mensuration — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSMensuration1 Mark
MCQ
A rectangular field with width of $80\ cm$ and a square field of side $120\ cm$ have same perimeter. Which one will be having a greater area?
  • A
    Both will have the same area.
  • B
    Rectangular field.
  • ✓
    Square field.
  • D
    Less information given.
✓

Answer

Correct option: C.
Square field.
C.  Square field.
Solution:
Perimeter of the square field $= 4 \times 120 = 480\ cm^2$
According to the question, both the fields have same perimeter.
$\therefore$ Perimeter of the rectangular field $= 2(length + 80)$
$\Rightarrow480 = 2(\text{l} + 80)$
$240 =$ length $+ 80$
Length $= 160\ cm$
Now, area of the square field $=$ side$^2 = 120^2 = 14400\ cm^2$
Area of the rectangular field $= l \times w = 160 \times 80 = 12800\ cm^2$
$\therefore$ Square field is having the greater area.

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