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ABCD- parallelogram, If the perimeter of Triangle CPQ is 15cm, Find the perimeter of triangle BAQ. Find the perimeter of triangl

melamori03 [73]

Answer:

The answer is below

Step-by-step explanation:

A parallelogram is a quadrilateral (has 4 sides and 4 angle) with two pair of parallel and opposite sides. Opposite sides of a parallelogram are parallel and equal.

Given parallelogram ABCD:

AB = CD = 18 cm; BC = AD = 8 cm

∠P = ∠P, ∠PDA = ∠PCQ (corresponding angles are equal).

Hence ΔPCQ and ΔPDA are similar by angle-angle similarity theorem. For similar triangles, the ratio of their corresponding sides equal. Therefore:

$\frac{CD}{PC}= \frac{AD}{CQ}\\\\\frac{18}{6}=\frac{8}{x} \\\\x=\frac{6*8}{18}=\frac{8}{3}\ cm$

Perimeter of CPQ = CP + CQ + PQ

15 = 6 + 8/3 + PQ

PQ = 15 - (6 + 8/3)

PQ = 6.33

∠CQP = ∠AQB (vertical angles), ∠QCP = ∠QBA (alternate angles are equal).

Hence ΔCPQ and ΔABQ are similar by angle-angle similarity theorem

$\frac{AQ}{QP}=\frac{AB}{CP} \\\\\frac{AQ}{6.33} =\frac{18}{6} \\\\AQ=\frac{18}{6}*6.33\\\\AQ = 19$

$\frac{BQ}{CQ}=\frac{AB}{CP} \\\\\frac{BQ}{8/3} =\frac{18}{6} \\\\BQ=\frac{18}{6}*\frac{8}{3} \\\\BQ =8$

Perimeter of BAQ = AB + BQ + AQ = 18 + 8 + 19 = 45cm

PA = AQ + PQ = 19 + 6.33 = 25.33

PD = CD + DP = 18 + 6 = 24

Perimeter of PDA = PA + PD + AD = 24 + 25.33 + 8 = 57.33 cm

7 0

2 years ago

Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day.

Serggg [28]

For this case we have a function of the form:
$y = A * (b) ^ x
$
Where,
A: initial amount
b: decrease rate
x: time in days
Substituting values we have:
$y = 40 * (0.85) ^ x
$
Therefore, the graph of the function is a decreasing exponential function in the first quadrant and that has an initial value of 40.
Answer:
graph of exponential function going from left to right in quadrant 1 through the point 0, 40 and approaching the x axis

7 0

2 years ago

Yolanda is planning out her square vegetable garden. One side 7 feet. How

Elan Coil [88]

Well if it’s a square all sides are equal, so all sides are 7ft.

Perimeter=
7+7+7+7=28ft
Or
7•4=28

Hope this helps!!!

3 0

2 years ago

Graph the function. Describe its position relative to the graph of the indicated function

sweet [91]

Answer:

C

Step-by-step explanation:

If the parent function is function $y=f(x)$ and $a>0,$ then

the graph of the function $y=f(x-a)$ is translated a units to the right graph of the parent function;
the graph of the function $y=f(x+a)$ is translated a units to the left graph of the parent function;
the graph of the function $y=f(x)+a$ is translated a units up graph of the parent function;
the graph of the function $y=f(x)-a$ is translated a units down graph of the parent function.

In your case, the grapgh of the function $y=2^x+2$ is translated 2 units up the graph of the function $y=2^x.$

6 0

2 years ago

Read 2 more answers

Determine whether the series is convergent or divergent. [infinity] n = 1 1 n√9 the series is a ---select--- p-series with p =

inna [77]

The series is a convergent p-series with p = 3

<h3>How to know it is a divergent or a convergent series</h3>

We would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.

The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.

The value of $\sqrt{9}= 3$

The formular for this is

∑ $\frac{1}{n^p} \\$

where n = 1

we know it is convergent because p is greater than 1. 3>1