Question

In triangle ABC ,BC=4cm,AD=7cm and BE=5cm. find the length of AC​

Answer 1

#answerwithquality #BAL

Answer 2

Length of side AC is 5.6 cm

Step-by-step explanation:

1. Given side of $\mathbf{\Delta ABC}$

  BC = 4 cm

  AC = find out

2. Altitude on side of $\mathbf{\Delta ABC}$

   AD = 7 cm  (which is altitude on side BC)

   BE = 5 cm  (which is altitude on side AC)

3. We know that area of triangle in side and altitude of triangle is

   $\mathbf{ar\Delta ABC=\frac{1}{2}\times (side\times altitude)}$

   We can write

   $\mathbf{ar\Delta ABC=\frac{1}{2}\times (AC\times BE)=\frac{1}{2}\times (BC\times AD)}$

   We can also write

   $\mathbf{\frac{1}{2}\times (AC\times BE)=\frac{1}{2}\times (BC\times AD)}$      ...1)

4. On putting respective value in above equation 1), we get

  $\mathbf{\frac{1}{2}\times (AC\times 5)=\frac{1}{2}\times (4\times 7)}$

 

   $\mathbf{AC\times 5=4\times 7}$

   So

   $\mathbf{AC= \frac{4\times 7}{5}=\frac{28}{5}=5.6 cm}$