In Delta ABC,P,Q,and R are the midpoints of A | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to the Midpoint Theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the

Vedclass · Accepted Answer

$13.8$

Vedclass · Answer

(A) According to the Midpoint Theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.In $\Delta ABC$,$P$ and $R$ are midpoints of $AB$ and $AC$ respectively,so $PR = \frac{1}{2} BC = \frac{9}{2} = 4.5 	ext{ cm}$.Similarly,$PQ = \frac{1}{2} AC = \frac{10.6}{2} = 5.3 	ext{ cm}$.And $QR = \frac{1}{2} AB = \frac{8}{2} = 4 	ext{ cm}$.The perimeter of $\Delta PQR = PQ + QR + PR = 5.3 + 4 + 4.5 = 13.8 	ext{ cm}$.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of $AB$,$BC$,and $AC$ respectively. If $AB = 8 \text{ cm}$,$BC = 9 \text{ cm}$,and $AC = 10.6 \text{ cm}$,find the perimeter of $\Delta PQR$ in $\text{cm}$.

Similar Questions

In trapezium $ABCD$,$AB \parallel CD$ and $E$ is the midpoint of $AD$. $A$ line drawn through $E$ and parallel to $AB$ intersects $BC$ at $F$. Prove that $F$ is the midpoint of $BC$ and $EF = \frac{1}{2}(AB + CD)$.

$ABC$ is a triangle right-angled at $C$. $A$ line through the mid-point $M$ of hypotenuse $AB$ and parallel to $BC$ intersects $AC$ at $D$. Show that $CM = MA = \frac{1}{2} AB$.

$E$ is the mid-point of a median $AD$ of $\triangle ABC$ and $BE$ is produced to meet $AC$ at $F$. Show that $AF = \frac{1}{3} AC$.

In $\Delta XYZ$,$A$ and $B$ are the midpoints of $XY$ and $XZ$ respectively. If $AB = 7.5 \, cm$,then find the length of $YZ$ in $cm$.

In $\Delta ABC$,the points $M$ and $N$ are on sides $AB$ and $AC$ respectively such that $AM = \frac{1}{4} AB$ and $AN = \frac{1}{4} AC$. Prove that $MN = \frac{1}{4} BC$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module