In Delta PQR,X, Y and Z are the midpoints of | vedclass

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(A) $1$. By the Midpoint Theorem,the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.$2$. G

Vedclass · Accepted Answer

Perimeter of $\Delta PQR = 23.2 \, cm$,Perimeter of $\Delta XYZ = 11.6 \, cm$

Vedclass · Answer

(A) $1$. By the Midpoint Theorem,the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.$2$. Given $X$ and $Z$ are midpoints of $PQ$ and $PR$,$XZ = \frac{1}{2} QR$. Thus,$QR = 2 	imes XZ = 2 	imes 3.8 \, cm = 7.6 \, cm$.$3$. Perimeter of $\Delta PQR = PQ + QR + PR = 7.2 \, cm + 7.6 \, cm + 8.4 \, cm = 23.2 \, cm$.$4$. Since $X, Y, Z$ are midpoints,$\Delta XYZ$ is formed by joining the midpoints,so its sides are half the lengths of the sides of $\Delta PQR$ ($XY = \frac{1}{2} PR = 4.2 \, cm$,$YZ = \frac{1}{2} PQ = 3.6 \, cm$,$XZ = 3.8 \, cm$).$5$. Perimeter of $\Delta XYZ = \frac{1}{2} 	imes (Perimeter \, of \, \Delta PQR) = \frac{1}{2} 	imes 23.2 \, cm = 11.6 \, cm$.

In $\Delta PQR$,$X, Y$ and $Z$ are the midpoints of $PQ, QR$ and $RP$ respectively. If $PQ = 7.2 \, cm$,$PR = 8.4 \, cm$ and $XZ = 3.8 \, cm$,then find the perimeter of $\Delta PQR$ and $\Delta XYZ$.

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