Question

One side of a rectangle is 12 cm long and its diagonal measures 37 cm. Find the other side and the area of the rectangle.

Answer 1

One side of the rectangle = 12 cm
Diagonal of the rectangle = 37 cm

The diagonal of a rectangle forms the hypotenuse of a right-angled triangle. The other two sides of the triangle are the length and the breadth of the rectangle.

Now, using Pythagoras' theorem, we have:

${\left(\mathrm{one}\mathrm{side}\right)}^2+{\left(\mathrm{other}\mathrm{side}\right)}^2={\left(\mathrm{hypotenuse}\right)}^2$
$$\begin{gathered} \Rightarrow {\left(12\right)}^2+{\left(\mathrm{other}\mathrm{side}\right)}^2={\left(37\right)}^2 \\ \Rightarrow 144+{\left(\mathrm{other}\mathrm{side}\right)}^2=1369 \\ \Rightarrow {\left(\mathrm{other}\mathrm{side}\right)}^2=1369-144 \\ \Rightarrow {\left(\mathrm{other}\mathrm{side}\right)}^2=1225 \\ \Rightarrow \mathrm{other}\mathrm{side}=\sqrt{1225} \\ \Rightarrow \mathrm{other}\mathrm{side}=35\mathrm{cm} \end{gathered}$$

Thus, we have:
Length = 35 cm
Breadth = 12 cm
$\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rectangle}=35\times 12=420{\mathrm{cm}}^2$