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4 years ago

Check my answer? The two triangles are similar. What is the value of x? 5.

Mathematics

1 answer:

Nikolay [14]4 years ago

4 0

20/28 = 3x / (4x + 2)

84x = 20(4x + 2)
84x - 80x = 40
4x = 40
x = 10

so the 2 lines are equal to 30 and 42

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The dimensions of a rectangular garden were 4m by 5m. Each dimension was increased by the same amount the garden then had an are

pogonyaev

The dimension of new garden is 7 meter by 8 meter

Solution:

The dimensions of a rectangular garden were 4m by 5m

Length = 4 m

Width = 5 m

Each dimension was increased by the same amount the garden then had an area of 56 square meter

Let "x" be the amount of increase

Then,

Length = 4 + x

Width = 5 + x

Also, given that,

New area = 56 square meter

The area of rectangle is given as:

$Area = length \times width$

Substituting the values we get,

$56 = (4+x)(5+x)\\\\56 = 20 + 4x + 5x + x^2\\\\x^2 + 9x + 20 - 56 = 0\\\\x^2 + 9x -36=0$

Let us solve the above equation by quadratic formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

$\text{For } x^2+9x-36 \text{ we get , }$

a = 1 and b = 9 and c = -36

Substituting the values of a = 1 ; b = 9 ; c = -36 in above quadratic formula we get,

$x = \frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-36\right)}}{2\cdot \:1}\\\\x = \frac{-9\pm \sqrt{81+144}}{2}\\\\x = \frac{-9 \pm 15}{2}$

We get two solutions,

$x = \frac{-9+15}{2} \text{ or } x = \frac{-9-15}{2}\\\\x = 3 \text{ or } x = -12$

Since dimension cannot be negative, ignore x = -12

Thus solution is x = 3

Length = 4 + x = 4 + 3 = 7

Width = 5 + x = 5 + 3 = 8

Thus dimension of new garden is 7 meter by 8 meter

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3 years ago

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4 years ago

Hello, i need to solve for x on this one

n200080 [17]

Answer:

x = 12.1532°

General Formulas and Concepts:

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] sinθ = opposite over hypotenuse
Inverse Trig

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = x

Opposite Leg = 4

Hypotenuse = 19

Step 2: Solve for x

Substitute in variables [sine]: sinx = 4/19
Inverse trig: x = sin⁻¹(4/19)
Evaluate: x = 12.1532°

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