Question

The diagonal BD of parallelogram ABCD is divided by segment AE in the ratio 1 : 2. If $BE = 1.8$ cm, find the length of AD.

Approach

The diagonal BD of parallelogram ABCD is divided by segment AE in the ratio $1 : 2$ . Given $BE = 1.8$ cm, find AD. In parallelogram, diagonals bisect each other at O. By BPT in similar triangles, $\frac{OB}{O D} = \frac{EB}{A D}$ . Since $\frac{A E}{E D} = \frac{1}{2}$ , and using properties of parallelogram, $A D = 3.6$ cm.

Step-by-step working

1
Prove $△ O A D \sim △ OEB$ by AA similarity criterion
1 mark
2
$\frac{OB}{O D} = \frac{EB}{A D}$ . Since diagonals bisect and ratio is $1 : 2$ , $\frac{1}{2} = \frac{1.8}{A D}$
0.5 marks
3
$A D = 2 \times 1.8 = 3.6$ cm
0.5 marks

Concepts used

parallelogramdiagonalratiobasic proportionality theoremfind length

Approach

Step-by-step working

Concepts used

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