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2 years ago

In JKL, mJ = 90, mK = 30, and mL = 60. Which of the following statements about JKL are true?

Mathematics

2 answers:

kumpel [21]2 years ago

8 0

The <em><u>correct answers</u></em> are:

KL = 2*JL; JK = (√3)JL; and JK = ((√3)/2)KL

Explanation:

This is a 30-60-90 right triangle. This type of triangle has a special relationship among the sides. Let the smallest side, across from the 30° angle, be t. This means JL = t.

The hypotenuse of the triangle is two times the length of the smallest side; this means that KL = 2t, which means that KL = 2*JL.

The side of the triangle opposite the 60° angle will be the "medium sized" side; it is equal to √3 times the smallest side, or √3t; this gives us that JK = √3t = (√3)JL.

Comparing JK to KL, we have

$\frac{t\sqrt{3}}{2t}$

The t on top and bottom cancel out, leaving us with the ratio (√3)/2. This means that JK = ((√3)/2)KL.

Llana [10]2 years ago

3 0

Jk=sqr3(JL)
KL-2(JL)
JK=(sqr3/2)KL

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A rectangle that had the perimeter of 70 and the area of 250 has enlarged; its sides became twice as long. what is the new area

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The perimeter of the original rectangle is:
P = 2w + 2l = 70
The area of the original rectangle is:
A = w * l = 250
Then, by modifying the length of its sides we have:
Perimeter:
P '= 2 (2w) +2 (2l)
Rewriting:
P '= 2 (2w + 2l)
P '= 2P
P '= 2 (70)
P '= 140
Area:
A '= (2w) * (2l)
Rewriting:
A '= (2) * (2) (w) * (l)
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P '= 140
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