Question

The diagonals of a rhombus is 7cm more than the other diagonal.if the area of rhombus is 15cm^ find the measure of each diagonal.

Answer 1

Answer:

measure of each diagonal is 11.5 cm.

Answer 2

First diagonal of rhombus is 3 cm and second diagonal is 10 cm.

Step-by-step explanation:

1. Let

  First diagonal $\mathbf{(d_{1})}$= d

  Then second diagonal $\mathbf{(d_{2})}$= d +7    (given)

2. Area of rhombus (A) = $\mathbf{15 (cm^{2})}$

3. We know that area of rhombus is

   $\mathbf{A=\frac{d_{1}\times d_{2}}{2}}$

 

   $\mathbf{\frac{d_{1}\times d_{2}}{2}=A}$

   

  $\mathbf{\frac{d\times (d+7)}{2}=15}$

  $\mathbf{d\times (d+7)=30}$      ...1)

4. Now equation 1) can be written as

   $\mathbf{d^{2}+7d-30=0}$

   from middle term splitting method

   $\mathbf{d^{2}+10d-3d-30=0}$

   $\mathbf{d(d+10)-3(d+10)=0}$

   So

   $\mathbf{(d-3)(d+10)=0}$       ...2)

5. Means

   $\mathbf{d-3=0}$            or   $\mathbf{d+10=0}$

   $\mathbf{d=3}$                   or   $\mathbf{d=-10}$

6. But diagonal can never be negative. So diagonal is 3 cm.

7.  First diagonal $\mathbf{(d_{1})}$= d= 3 (cm)

  Then second diagonal $\mathbf{(d_{2})}$= d +7 = 3+7 =10 (cm)

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