1.

17. The measure of the height AD of a ABC with respect to the base BCis 4 cm. P is a point on BC such that BP = 3 cm. and arABP = arAPC.Find the measure of PC.​

Answer»

<P>Answer:

The measure of PC is 3 cm

Step-by-step explanation:

given : AD = 4 cm

we have to find the measure of PC

given that the AREA of triangle ABP= area of triangle APC.

therefore ,

area of triangle ABP

\begin{gathered}= \frac{1}{2}\times base \times height \\\\= \frac{1}{2}\times BP \times AD\end{gathered}

=

2

1

×base×height

=

2

1

×BP×AD

similarly area of triangle APC

\begin{gathered}= \frac{1}{2}\times base \times height \\\\= \frac{1}{2}\times PC \times AD\end{gathered}

=

2

1

×base×height

=

2

1

×PC×AD

Since , area of triangle ABP= area of triangle APC

\frac{1}{2}\times BP \times AD = \frac{1}{2}\times PC \times AD

2

1

×BP×AD=

2

1

×PC×AD

BP = PC

thus the value of PC = 3 cm

#LEARN more:

In triangle abc, p is a point on bc such that bp: pc = 2 : 3 and is the MIDPOINT of bp. then (area of triangle abq) : (area of triangle abc) is equal to:

Step-by-step explanation:

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