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hram777 [196]
3 years ago
15

The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find t

he side lengths of the triangle
Mathematics
1 answer:
Alexeev081 [22]3 years ago
8 0
Longer leg = x + 4

Shorter leg = x

Hypotenuse = x + 8


Using Pythagorean Theorem:

a^2 + b^2 = c^2

(x + 4)^2 + x^2 = (x + 8)^2

x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

2x^2 + 8x + 16 = x^2 + 16x + 64

2x^2 +8x = x^2 + 16x + 48

2x^2 - 8x = x^2 + 48

x^2 - 8x = 48

x^2 - 8x - 48 = 0

You can complete the square from here or use the quadratic formula.

Completing the square:

x^2 - 8x = 48

x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2

x^2 - 8x + 16 = 48 + 16

(x - 4)(x - 4) = 64 or (x - 4)^2 = 64

x - 4 = +√64 OR x - 4 = -√64

x - 4 = +8 OR x - 4 = -8

x = 12 OR x = -4

However, you can't use negative 4 as a length because your length needs to be a positive.

So x will be 12.


Shorter leg: 12

Longer leg: 12 + 4

Hypotenuse: 12 + 8

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daser333 [38]

Option D:

A = 1, B = –3 and C = 4.

Solution:

Given equation is x – 3y + 4 =0.

General equation of a line format:

<em>Ax + By + C = 0</em>

<u>To identify A, B and C in the given equation:</u>

x – 3y + 4 =0 is a equation of a line which is in the form of Ax + By + C = 0.

That is,

The coefficient of x is A ⇒ A = 1

The coefficient of y is B ⇒ B = –3

The constant term is C ⇒ C = 4

A = 1, B = –3 and C = 4.

Hence Option D is the correct answer.

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Given:

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Central angle = x

To find:

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Solution:

We have,

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\theta = x

We know that, area of a sector is

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\dfrac{24\pi}{144\pi}=\dfrac{x}{360^\circ}

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The value of x is 60 degrees.

Therefore, the correct option is A.

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Answer:

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