Question

In triangle XYZ,M and N are midpoints of XY and XZ respectively P and Q are midpoints of XM and XN if PQ=2.8cm find the length of YZ

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{In triangle XYZ,}$

$\textsf{M and N are midpoints of XY and XZ}$

$\textsf{P and Q are midpoints of XM and XN and PQ=2.8cm}$

$\underline{\textsf{To find:}}$

$\textsf{Length of YZ}$

$\underline{\textsf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\boxed{\begin{minipage}{9cm} \;\;\\\textsf{A line segment joining midpoints of two sides of a triangle is}\\\\\textsf{parallel to the third side and half of it}\\ \end{minipage}}$

$\mathsf{In\;\triangle\,XMN}$

$\mathsf{PQ{\parallel}MN\;\;and}$

$\mathsf{PQ=\dfrac{1}{2}{\times}MN}$

$\mathsf{2.8=\dfrac{1}{2}{\times}MN}$

$\implies\mathsf{MN=2{\times}2.8}$

$\implies\boxed{\mathsf{MN=5.6\,cm}}$

$\mathsf{In\;\triangle\,XYZ}$

$\mathsf{MN{\parallel}YZ\;\;and}$

$\mathsf{MN=\dfrac{1}{2}{\times}YZ}$

$\mathsf{5.6=\dfrac{1}{2}{\times}YZ}$

$\implies\mathsf{YZ=2{\times}5.6}$

$\therefore\boxed{\mathsf{YZ=11.2\,cm}}$

$\underline{\textsf{Find more:}}$

Answer 2

Answer:

YZ = 11.2

Step-by-step explanation:

In triangle XMN,

P is the midpoint of XM

Q is the midpoint of XN

PQ//MN and PQ = 1/2 MN ...by midpoint theorem

MN = 2PQ

MN = 2(2.8)

MN = 5.6 cm

In triangle XYZ,

M is the midpoint of XY

N is the midpoint of XZ

MN//YZ and MN = 1/2 YZ ...by midpoint theorem

YZ = 2MN

YZ = 2(5.6)

YZ = 11.2 cm