Question

A parallelogram whose sides are 10 cm and 5 cm has one diagonal of 8 cm, then the length of the other diagonal is

• A. $12cm$
• B. $11cm$
• C. $14cm$
• D. None of these

Answer 1

The correct option is D None of these

We will find the area of $△ADC$ by heron's formula.
$s=\frac{5+10+8}{2}=\frac{23}{2}=11.5cm$
$Areaof△ADC=\sqrt{1}1.5(11.5-5)(11.5-10)(11.5-8)$
$=19.81$
Now, $areaof△ADC=areaof△BDC$(as triangles on same base and between same parallels are equal in area)
$So,areaof△BDC=19.81$
$=\frac{1}{2}\times 4\times BD=19.81$
On solving we get $BD=9.9cm$
So, the other diagonal is 9.9cm