Question:
The length of a rectangular field is 12 m and the length of its diagonal is 15 m. The area of the field is
(a) 108 m2
(b) 180 m2
(c) $30 \sqrt{3} \mathrm{~m}^{2}$
(d) $12 \sqrt{15} \mathrm{~m}^{2}$
Solution:
(a) 108 m2
Length of the rectangular field = 12 m
Diagonal = 15 m
Diagonal $^{2}=$ Length $^{2}+$ Breadth $^{2}$
Breadth $=\sqrt{\text { Diagonal }^{2}-\text { Length }^{2}}$
$=\sqrt{15^{2}-12^{2}}$
$=\sqrt{225-144}$
$=9 \mathrm{~m}$
$\therefore$ Area of the field $=$ Length $\times$ Breadth $=12 \times 9=108 \mathrm{~m}^{2}$
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