Question

In triangle ABC ,P and Q are the mid points of AB and AC .P and Q are joined .If

PQ=3.5cm, then find the length of BC.

(Please ans As per Mid Point Theorem)​

Answer 1

Given:

In ΔABC,

P and Q are midpoints of AB and AC

P and Q are joined

PQ = 3.5 cm

To find:

The length of BC

Solution:

We know,

$\boxed{\underline {\bold{Mid-point \:Theorem}}}:$ This theorem states that the line segment joining the two sides of a triangle at the midpoints of those two sides is half the length of the third side.

According to the theorem above, we can write as,

$PQ = \frac{1}{2}\times BC$

by substituting the value of PQ = 3.5 cm

$\implies 3.5 = \frac{1}{2}\times BC$

$\implies BC = 3.5 \times 2$

$\implies \bold{BC = 7\:cm}$

Thus, the length of BC is 7 cm.

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