Question

In triangle ABC AB equals to 8 cm if the altitude corresponding to a b and b c are 4 cm and 5 cm respectively find area of triangle ABC and the length of BC

Answer 1

I hope u will satisfy with this

Answer 2

Length of BC = 6.4 (cm)

Step-by-step explanation:

1. In $\mathbf{\Delta ABC}$

  AB= 8 (cm)

  Let BC = x (cm)

  Altitude on AB $\mathbf{P_{1}=4(cm)}$

  Altitude on BC $\mathbf{P_{2}=5(cm)}$

2. Area of triangle $\mathbf{=\frac{1}{2}\times side\times altitude}$

  So

 Area of triangle $\mathbf{=\frac{1}{2}\times AB\times P_{1}==\frac{1}{2}\times BC\times P_{2}}$      ...1)

3. Equation 1) can also be written as

  $\mathbf{\frac{1}{2}\times AB\times P_{1}==\frac{1}{2}\times BC\times P_{2}}$

   $\mathbf{\frac{1}{2}\times 8\times 4=\frac{1}{2}\times x\times 5}$

  On  solving

  $\mathbf{x=\frac{8\times 4}{5}=6.4 (cm)}$

4. Where x is value of side BC. So BC is 6.4 (cm)