One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm², find the length of the shorter diagonal.                                                                                                                                            [Page No. 142]

Let shorter diagonal $d_1 = x$

Longer diagonal $d_2 = 2x$

Area of rhombus:

$$A = \frac{1}{2} d_1 d_2$$

$$128 = \frac{1}{2} (x)(2x)$$

$$128 = x^2$$

$$x = \sqrt{128} = 8\sqrt{2}$$

Concept Applied
The area of a rhombus is half the product of its diagonals is $\frac{1}{2} \times d_{1} \times d_{2}$.