Question

If the sum of diagonals of a rhombus is $10$ cm and its area is $12$ $c{m}^2$ Then the length of its diagonals are :

• A. $5,5$
• B. $9,1$
• C. $8,2$
• D. $6,4$

Answer 1

The correct option is D $6,4$

Let $d_1$ and $d_2$ be the diagonals of rhombus

Now, $d_1+d_2=10㎝\to 1$

Area of rhombus$=\frac{1}{2}\times d_1\times d_2=12㎠$

$\Rightarrow d_1{d}_2=24㎠\to 2$

From $1,d_2=10-d_1$, Put in $2$

$d_1(10-d_1)=24$

$10d_1-d_1^2=24$

$d_1^2-10d_1+24=0$

$(d_1-6)(d_1-4)=0\Rightarrow d_1=4$ & $6$

If $d_1=4,d_2=10-4=6$ and if $d_1=4,d_2=10-6=4$