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3 years ago

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1 answer:

____ [38]3 years ago

6 0

Answer:

(0,0) (1,2)

Step-by-step explanation:

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

Number 13 please. I know the answer is 20 I just don’t know how to get there

Rudiy27

4/20 is 0.20, which is equivalent to 20%.

Remember that 1.0=100%, 0.5=50%, 0.2=20%, 0.05=5%, and so on.

4 0

3 years ago

Read 2 more answers

HELP HELLP HELP MEH I NEED 16 MORE CLASSES LEFT FOR SCHOOL LET IT BECOME 15 PLEASE

vodomira [7]

Answer:

2*2*9+4*12*3=36+144=180

Step-by-step explanation:

8 0

3 years ago

The product of 15 and the sum of a number and 5 expression

Sedbober [7]

(15)(x+5) because product means multiply the two terms tigether

7 0

2 years ago

I need help with similar triangles

Alika [10]

Answer:

ΔGHI and ΔDEF are similar by SSS criteria

Step-by-step explanation:

Consider triangle GHI and triangle DEF

In ΔGHI, GH = 2, HI =4 and GI = 3.5

In ΔDEF , DE =4, EF = 6 and DF = 7

GH/DE = 2/4 =1/2

HI/EF = 3/6 = 1/2

GI/DF = 3.5/7 = 1/2

The corresponding sides are in same ratio by SSS criteria

ΔGHI and ΔDEF are similar

5 0

3 years ago