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) 180 m²
(b) $30\sqrt{3}{\mathrm{m}}^2$
(c) $12\sqrt{15}{\mathrm{m}}^2$
(d) none of these

Answer 1

(d) none of these

Length of the rectangular field = 12 m
Diagonal = 15 m


${\mathrm{Diagonal}}^2={\mathrm{Length}}^2+{\mathrm{Breadth}}^2$
$$\begin{gathered} \mathrm{Breadth}=\sqrt{{\mathrm{Diagonal}}^2-{\mathrm{Length}}^2} \\ =\sqrt{{15}^2-{12}^2} \\ =\sqrt{225-144} \\ =9\mathrm{m} \end{gathered}$$

∴ Area of the field$=\mathrm{Length}\times \mathrm{Breadth}=12\times 9=108{\mathrm{m}}^2$