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

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

Question

(B) Given that $P$, $Q$, and $R$ are the midpoints of $AB$, $BC$, and $CA$ respectively.By the Midpoint Theorem, the line segment joining the midpoint

Vedclass · Accepted Answer

$14.6$

Vedclass · Answer

(B) Given that $P$, $Q$, and $R$ are the midpoints of $AB$, $BC$, and $CA$ respectively.By the Midpoint Theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.In $\Delta ABC$, $R$ is the midpoint of $AC$ and $Q$ is the midpoint of $BC$. Thus, $RQ = \frac{1}{2} AB = \frac{8.2}{2} = 4.1 	ext{ cm}$.Also, $P$ is the midpoint of $AB$ and $Q$ is the midpoint of $BC$. Thus, $PQ = \frac{1}{2} AC = \frac{7.5}{2} = 3.75 	ext{ cm}$.Since $P$ is the midpoint of $AB$, $PB = \frac{1}{2} AB = \frac{8.2}{2} = 4.1 	ext{ cm}$.Since $Q$ is the midpoint of $BC$, $BQ = \frac{1}{2} BC = \frac{6.4}{2} = 3.2 	ext{ cm}$.The quadrilateral $PBQR$ has sides $PB$, $BQ$, $QR$, and $RP$.Perimeter $= PB + BQ + QR + RP$.We know $RP = \frac{1}{2} BC = 3.2 	ext{ cm}$.Perimeter $= 4.1 + 3.2 + 4.1 + 3.2 = 14.6 	ext{ cm}$.

In $\Delta ABC$, $P$, $Q$, and $R$ are the midpoints of $AB$, $BC$, and $CA$ respectively. If $AB = 8.2 \text{ cm}$, $BC = 6.4 \text{ cm}$, and $CA = 7.5 \text{ cm}$, then find the perimeter of quadrilateral $PBQR$. (in $\text{ cm}$)

Similar Questions

In quadrilateral $ABCD$,$\angle A + \angle D = 180^{\circ}$. What special name can be given to this quadrilateral?

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $BC + PQ = 21 \text{ cm}$,then find the length of $BC$.

$(1)$ $A$ quadrilateral in which only one pair of opposite sides are parallel is a $\ldots \ldots \ldots$.
$(2)$ The diagonals of a rectangle are $\ldots \ldots \ldots$.

Can all the angles of a quadrilateral be right angles? Give reason for your answer.

The angles of a quadrilateral are in the ratio $3:4:6:5$. Find the measure of the greatest angle. (in $^\circ$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module