Question

In a ΔABC, D, E and F are, respectively, the mid points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ΔDEF.

Answer 1

The perimeter of ΔDEF is 12 cm.

Step-by-step explanation:

Given:

Here in a ΔABC, D, E and F are the mid points of BC, CA and AB respectively.

Also AB = 7 cm, BC = 8 cm, AC = 9 cm

Now, using Midpoint Theorem, we get

$EF = \frac{1}{2}BC, DF = \frac{1}{2} AC, DE = \frac{1}{2}AB$

Perimeter of ΔDEF = DE + EF + DF

                               = $\frac{1}{2}AB + \frac{1}{2}BC +\frac{1}{2}AC$

                               = $\frac{1}{2}[7+8+9]$

                               = $\frac{24}{2}$

                               = 12 cm

Therefore the perimeter of ΔDEF is 12 cm.

Answer 2

Answer:

the perimeter of ΔDEF is 12 cm.

Step-by-step explanation:

By using Midpoint Theorem, we get

Perimeter of ΔDEF = DE + EF + DF

                               =1/2AB+1/2BC+1/2AC

                               =1/2(7+8+9)

                               =24/2

                                =12cm