Question

Find QP using given information in the figure.

MN = 25 units, MQ = 14 units and NP = 40

units.​

Answer 1

SOLUTION

GIVEN

In the figure MN = 25 units, MQ = 14 units and NP = 40 units.

TO DETERMINE

The length of QP

CONCEPT TO BE IMPLEMENTED

ANGLE BISECTOR THEOREM

An angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle

EVALUATION

In the figure it is given that MN = 25 units, MQ = 14 units and NP = 40 units.

Now QN is the angle bisector of the angle N

So by the Angle Bisector Theorem

$\displaystyle \sf{ \frac{NP}{MN} = \frac{QP}{MQ} }$

$\displaystyle \sf{ \implies \frac{40}{25} = \frac{QP}{14} }$

$\displaystyle \sf{ \implies QP = \frac{40 \times 14}{25} }$

$\displaystyle \sf{ \implies QP = 22.4 }$

Hence the length of QP is 22.4 unit

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