Question

If ABCD is a rectangle. If the diagonals are of the length (8x - 9) cm and (3x + 6) cm, then find the length of the diagonal.

• A. 3 cm
• B. 10 cm
• C. 15 cm
• D. 18 cm

Answer 1

The correct option is C 15 cm


ABCD is a rectangle. Hence the lengths of the diagonals are equal.
$\Rightarrow (8x-9)=(3x+6)=8x-9=3x+6=8x-3x=6+9=5x=15\Rightarrow x=\frac{15}{5}=3$

$8x-9$ is the length of the diagonal.
$\Rightarrow 8\times 3-9=24-9=15$

$\therefore$ The length of the diagonal is 15 cm.