Question

In ΔPQR, PQ = 5 cm, QR = 12 cm, PR = 13 cm. M and N are mid-points of PQ and QR. The length of MN is ______.

पर्याय

• 2.5 cm

• 6 cm

• 6.5 cm

• none of these

Answer 1

In ΔPQR, PQ = 5 cm, QR = 12 cm, PR = 13 cm. M and N are mid-points of PQ and QR. The length of MN is 6.5 cm.

Explanation:

In triangle ΔPQR, we are given:

• PQ = 5 cm,
• QR = 12 cm,
• PR = 13 cm,
• M and N are midpoints of sides PQ and QR, respectively.

We are asked to find the length of segment MN.

Step 1: Apply the Midpoint Theorem:

The Midpoint Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the length of that third side.

In this case:

• M is the midpoint of PQ,
• N is the midpoint of QR.

So, segment MN is parallel to side PR and is half of its length.

Therefore, the length of MN is

`MN = 1/2 xx PR`

= `1/2 xx 13` cm

= 6.5 cm