Question

The ratio of the lengths of the sides of △ABC is 2:3:4. Points M, N, and K are the midpoints of the sides. Perimeter of △MNK equals 7.2 in. Find the length of the sides of △ABC. No picture

Answer 1

Answer: Hence, the length of sides will be 3.2 in, 4.8 in., 6.4 in.

Explanation:

Since we have given that

Ratio of lengths of the sides of ΔABC is 2:3:4

So, the length of first side 'AB' be 2x

Length of second side 'BC' be 3x

Length of third side 'AC' be 4x

Now, we have given that M,N,K are the midpoints of the sides ,

As shown in the figure below:

As we know the Mid-point theorem which states that the line joining the midpoints is always parallel to the third side and half to the third side too.

So by applying this we get,

Length of MN is given by

$\frac{4x}{2}=2x$

Length of NK is given by

$\frac{2x}{2}=x$

Length of MK is given by

$\frac{3x}{2}=1.5x$

Also, we have given that perimeter of ΔMNK is 7.2 in.

So,

$MN+NK+MK=7.2\\x+2x+1.5x=7.2\\4.5x=7.2\\x=1.6$

So, the length of AB is given by

$2x=2\times 1.6=3.2\ in.$

Length of AC is given by

$3x=3\times 1.6=4.8\ in.$

Length of BC is given by

$4x=4\times 1.6=6.4\ in.$

Hence, the length of sides will be 3.2 in, 4.8 in., 6.4 in.