Question

if median AM of triangle ABC is 3.5 cm and median PN of triangle PQR is 4.0 CM if area of triangle ABC is 49 CM square find the area of triangle PQR

Answer 1

please see image
it is the correct ans..

Answer 2

Area of $\mathbf{\Delta PQR}$ is 64 $(cm^{2})$

Step-by-step explanation:

1. Given data

  Median AM = 3.5 (cm)

  Area of triangle ABC $\mathbf{=ar\Delta ABC=49 (cm^{2})}$

  Median PN = 4.0 (cm)

2. From relation between area and median of two similar triangle is given below

  $\mathbf{\frac{ar\Delta PQR}{ar\Delta ABC}=\left ( \frac{PN}{AM} \right )^{2}}$

 Which can also be written as

 $\mathbf{ar\Delta PQR=\left ( \frac{PN}{AM} \right )^{2}\times ar\Delta ABC}$      ...1)

3. From equation 1)

  $\mathbf{ar\Delta PQR=\left ( \frac{PN}{AM} \right )^{2}\times ar\Delta ABC}$

 

  $\mathbf{ar\Delta PQR=\left ( \frac{4}{3.5} \right )^{2}\times 49}$

 

 On solving above equation, we get

  $\mathbf{ar\Delta PQR=64(cm^{2}) }$