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Luba_88 [7]
2 years ago
5

In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

of the triangle DBC.

Mathematics
1 answer:
Ivan2 years ago
4 0
Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}

The base x is 4, the height h is 3/5. Calculate the area:

A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}

The area of triangle DBC is 6/5.

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Answer:

11/12

Step-by-step explanation:

1/4+2/3

1/4×3/3+2/3×4/4

3/12+8/12

8 0
3 years ago
An online furniture store sells chairs for $200 each and tables for $600 each. Every
Vladimir79 [104]

Answer:

Step-by-step explanation:

Answer:

If the minimum 13 chair were sold , then the minimum number of Table sold is 14

Step-by-step explanation:

Given as :

The cost of each chair = $ 200

The cost of each table = $ 600

The total number of furniture sold per day = 32

The minimum amount of selling per day = $ 12000

Let the total number of chair = C

The total number of table = T

So , according to question

C + T = 32         .......1

200 C + 600 T = 12000         .......2

Solving eq 1 and 2

200 C + 600 T = 12000

200 × ( C + T ) = 32 × 200

I.e 200 C + 200 T = 6400

or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 6400

Or, 400 T =  5600

∴  T =

I.e T = 14

Put The value of T in eq 2

So, 200 C + 600 × 14 = 12000

or , 200 C + 8400 = 12,000

Or, 200 C = 12000 - 8400

Or, 200 C = 3600

∴   C =

I.e C = 18

The number of chair sold is 18

If the number of chair sold is 13 ,

Then the min number of table sold = 200 × 18 + 600 T = 12000

i.e 600 T = 12000 - 3600

or, 600 T = 8400

∴   T =

I.e T = 14

Hence if the minimum 13 chair were sold , then the minimum number of Table sold is 14 . Answer

8 0
3 years ago
The population of Tinyville is 16.2 Tinys per acre. Exactly 405 Tinys live in Tinyville. How many acres is Tinyville? Only enter
Mice21 [21]
The answer is 25 because 405/16.2=25.
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3 years ago
Describe the translation from f ( x ) = I x I... to f ( x ) = I x - 1 I + 11.
noname [10]
Horizontal shift 1 unit left and vertical shift 11 units up
6 0
2 years ago
Which equation represents this number sentence?<br> Two more than one-third of a number is 8
Alja [10]

Answer:

Step-by-step explanation:

One - third = 1/3

then:

one third of a number = a*1/3 = a/3

Then the equation that represents this sentence is:

2 + a/3 = 8

process:

a/3 = 8 - 2

a/3 = 6

a = 6*3

a = 18

Check:

2 + 18/3 = 8

2 + 6 = 8

3 0
1 year ago
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