Question

The breadth of the rectangle is 8 cm and its diagonal BD is 17 cm. Find the area of the rectangle and its perimeter.

• A. 120 cm², 46 cm
• B. 110 cm², 46 cm
• C. 120 cm², 23 cm
• D. 110 cm², 23 cm

Answer 1

The correct option is A

120 cm², 46 cm

Using Pythagoras theorem in $\Delta$BCD,

BD${}^2$= DC${}^2$+ BC${}^2$

17${}^2$ = DC${}^2$+ 8${}^2$

289 - 64 = DC${}^2$

225 = DC${}^2$

15 = DC

Therefore, length of rectangle = 15 cm

So, area of rectangle = l $\times$ b

= 15 cm $\times$ 8 cm

= 120 cm${}^2$

Also, perimeter of rectangle = 2 $\times$ (15 + 8) cm

= 2 $\times$ 23 cm

= 46 cm