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3 years ago

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If the legs of a right triangle are given by x2 - y2 and 2xy, then which expression equals the hypotenuse? choose all that apply

. x2 y2 (x2 y2)2 (x2 - y2)2 (2xy)2

1 answer:

11Alexandr11 [23.1K]3 years ago

3 0

Hypothenus = sqrt ((x^2 - y^2)^2 + (2xy)^2) = sqrt(x^4 - 2x^2y^2 + y^4 + 4x^2y^2) = sqrt(x^4 + 2x^2y^2 + y^4) = sqrt(x^2 + y^2)^2 = x^2 + y^2

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3 years ago

the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

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Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}$

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

$\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}$

On solving the above expression for x we get

$\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}$

$\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}$

Hence length and width of rectangle is 15 inches and 6 inches.

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IgorLugansk [536]

So, we know that:

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We also know that $(a+b)^2=a^2+2ab+b^2$ . We will use that fact to find $c$ in terms of $A$ and $P$ .

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Answer:

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