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AnnZ [28]
2 years ago
11

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find

the side lengths of the
triangle.
cm
Length of the shorter leg: 0
Length of the longer leg: 0
Length of the hypotenuse: 0
cm
cm
Mathematics
1 answer:
Andrews [41]2 years ago
7 0

Answer:

Shorter leg = 20 cm.

Longer leg = 21cm.

Hypotenuse = 29 cm

Step-by-step explanation:

Let the shorter leg be x cm long

Then longer leg = x + 1 and hypotenuse = x + 9 cm long

So by Pythagoras:

x^2 + (x + 1)^2 = (x + 9)^2

0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)

x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0

-x^2 + 16x + 80 = 0

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

So x = 20   (we ignore the negative root).

So longer leg = 20 + 1 and hypotenuse = 20 + 9.

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devlian [24]

Answer: Yes these triangles are similar

Step-by-step explanation:

First lets write down what we know just to make life easier

x=9

TL should be similar to CH

LY should be similar to KH

The angles should be equal due to SAS

So the first thing we know is true is the fact that they have equal angles. Now we have to find out if the sides are similar or if they change by the same ratio to the other. If TL is similar to CH and TL=25  and CH=10 what is the change in size or dilation. Division should do the trick so 25/10=2.5 so TY is greater than CH by a factor of 10. Which means that LY should also be greater than KH by a factor of 2.5. If we are told that x=9 than side LY or 4(9)-1=35 and KH 9+5=14

So side KH is 14 and LY is 35. Now to check if they are similar then KH should be greater by a factor of 2.5. If this is not true than the sides are not similar.  35/2.5=14

Since 35 divided by 2.5 is 14 we can tell both sides TL and LY are greater than KH and CH by a factor of 2.5

Hope this helps.

8 0
3 years ago
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4 0
3 years ago
A poll found that 53% of a sample of 1170 teens in a certain large country go online several times a day. (Treat this sample as
posledela

Answer:(a) margin error = 2.4%

(b) The margin error gives the measure in percentage of how the population parameter determined differ from the real population statistics or value.

(c) in 90% of the samples of teens in the country, the percent who go online several times a day will be within 50.6% and 55.4%. of the estimated 100%

Step-by-step explanation:

Using the proportion formulae

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