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3 years ago

Question #2

Mathematics

1 answer:

Elanso [62]3 years ago

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A triangle has an area of 38.4 cm2. The

lisov135 [29]

Answer:

6cm

Step-by-step explanation:

$A = \frac{h_b b}{2}$

$38.4 = \frac{12.8_b b}{2}$

$b = 2\frac{A}{h_b}$

$b = 2\frac{38.4}{12.8}$ = 6

8 0

2 years ago

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

A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 5x − 5 and EC = 3x + 9, find the distance between

Montano1993 [528]

Answer:

C. 60 ft

Step-by-step explanation:

If triangles ABC and EDC are in a 1:1 relation, they are congruent, and

AC = EC

5x - 5 = 3x + 9

5x = 3x + 14

2x = 14

x = 7

AC = 5x + 5 = 5(7) - 5 = 35 - 5 = 30 ft

EC = 3x + 9 = 3(7) + 9 = 21 + 9 = 30 ft

Distance between top and bottom of bridge = AC + EC = 30 + 30 = 60 ft

5 0

3 years ago

Read 2 more answers

Y= 2? + 16x + 64<br> 1. Identify a, b, and c<br> b=<br> C=

liraira [26]

ask a tutor for help with that my dude I don't know sorry

5 0

2 years ago

What do I do when the output doesn't have a constant rate of change?

Solnce55 [7]

-2 gal/min

sry if it wrong

3 0

2 years ago