10 points each! PLZ HELP SOLVE THIS PROBLEM ASAP! and show your work.

Practice question — Given the trapezoid to the right find the length of legs in the following isosceles trapezoid

ad-work [718]

Given:

A figure of an isosceles trapezoid with bases 18 and 24, and the vertical height is 4.

To find:

The legs of the isosceles trapezoid.

Solution:

Draw another perpendicular and name the vertices as shown in the below figure.

From the figure it is clear that the AEFD is a rectangle. So,

$EF=AD=18$

Since ABCD is an isosceles trapezoid, therefore in triangle ABE and DCF,

$AB=DC$ (Legs of isosceles trapezoid)

$AE=DF$ (Vertical height of isosceles trapezoid)

$m\angle AEB=m\angle DFC$ (Right angle)

$\Delta ABE\cong \Delta DCF$ (HL postulate)

$BE=CF$ (CPCTC)

Now,

$BE+EF+FC=BC$

$2BE+18=24$

$2BE=24-18$

$2BE=6$

$BE=3$

Using Pythagoras theorem in triangle ABE, we get

$Hypotenuse^2=Perpendicular^2+Base^2$

$(AB)^2=(AE)^2+(BE)^2$

$(AB)^2=(4)^2+(3)^2$

$(AB)^2=16+9$

$(AB)^2=25$

Taking square root on both sides, we get

$AB=\pm \sqrt{25}$

$AB=\pm 5$

Side length cannot be negative. So, $AB=5$ .

Therefore, the length of legs in the given isosceles trapezoid is 5 units.

3 0

3 years ago

A shipping container holds 20 soft drink boxes. The dimensions of a soda box are 15 inches by 4 inches by 5 inches. What is the

patriot [66]

Answer:

6000 in³

Step-by-step explanation:

To solve this problem, we simply have to find the volume of the shipping container that will be just enough to contain the 20 soda boxes.

To do this, we find the volume of each soda box and multiply it by the total number of soda boxes held by the shipping container.

Volume of the box = L * B * H

L = length = 15 in

B = breadth = 4 in

H = height = 5 in

V = 15 * 4 * 5 = 300 in³

This is the volume of each soda box.

The volume of 20 soda boxes will then be:

V = 20 * 300 = 6000 in³

This is the volume of 20 soda boxes and hence, the minimum size the shipping container can be.

7 0

4 years ago

Simon makes 30 cakes. He gives of the cakes to Sali. He gives 10% of the 30 cakes to Jane. 5 What fraction of the 30 cakes does

Novosadov [1.4K]

1/5 = 0.2 = 20%

100% - 20% - 10% = 70%

He left 70%

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6 0

3 years ago

A barber has already cut for peoples hair today. Every 10 minutes another person comes to the Barber to get a haircut. Write

Alexeev081 [22]

Answer:

Ans. (1) For preparing vaccines, in olden days,microbes were injected in the bodies of horses ormonkeys. These laboratory animals used to makeantibodies to defend these microbes. Antibodies areproteins which can act against the disease-causinggerms. These antibodies were extracted from theblood of these animals and were used as vaccines.(2) Now-a-days with the advent of biotechnology,the vaccines are manufactured in laboratories withthe help of bacteria. For this purpose, a detailedstudy of the disease causing germ is undertaken.The genes and the DNA of such microbes arethoroughly explored. Then based on thisinformation, proteins which can act against suchmicrobes are synthetically prepared in thelaboratories. The safe vaccine is produced in such away which can defend the body against infections.3) Some types of vaccines are prepared from theextracts of germs. These germs or microbes aredeactivated and made dormant. When they areinjected in the body of a person, they initiate thedefending action. The body of such vaccinatedperson, already develops the antibodies in his or herbody. When in future, this person is again attackedby similar germs the defence starts immediately andthe person does not become sick.

7 0

3 years ago

What are the solutions to 16x -12x+0=54?

Citrus2011 [14]

Answer:

x = 13 1/2

Step-by-step explanation:

16x -12x+0=54

combine like terms

4x + 0 = 54

4x = 54

divide each side by 4

4x/4 = 54 /4

x = 54/4

x = 13 2/4

x = 13 1/2

8 0

3 years ago