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Anettt [7]
2 years ago
11

In a triangle ABC, measure of angle B is 90 degrees. AB is 3x-2 units and BC is x+3. If the area of the triangle is 17 sq cm, fo

rm an equation in terms of x and solve it.​
Mathematics
1 answer:
Scorpion4ik [409]2 years ago
6 0

Answer:

x=\frac{8}{3}\ cm

Step-by-step explanation:

we know that

The area of the right triangle ABC is equal to

A=\frac{1}{2}(AB)(BC)

we have

A=17\ cm^2

AB=(3x-2)\ cm

BC=(x+3)\ cm

substitute the values

17=\frac{1}{2}(3x-2)(x+3)

34=(3x-2)(x+3)

34=3x^2+9x-2x-6

3x^2+7x-6-34=0

3x^2+7x-40=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

3x^2+7x-40=0

so

a=3\\b=7\\c=-40

substitute in the formula

x=\frac{-7(+/-)\sqrt{7^{2}-4(3)(-40)}} {2(3)}

x=\frac{-7(+/-)\sqrt{529}} {6}

x=\frac{-7(+/-)23} {6}

x=\frac{-7(+)23} {6}=\frac{16}{6}=\frac{8}{3}

x=\frac{-7(-)23} {6}=-5

therefore

The solution is

x=\frac{8}{3}\ cm

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<h2>Hello!</h2>

The answers are:

The possible values for x in the equation, are:

First option, 5\sqrt[3]{3}

Second option,  \sqrt[3]{375}

<h2>Why?</h2>

To solve the problem, we need to remember the following properties of the exponents and roots:

a\sqrt[n]{b}=\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{a^{m} }=a^{\frac{m}{n}}\\\\(a^{b})^{c}=a^{b*c}

Then, we are given the expression:

x^{3}=375

So, finding "x", we have:

x^{3}=375\\\\(x^{3})^{\frac{1}{3} } =(375)^{\frac{1}{3}}\\\\x=\sqrt[3]{375}=\sqrt[3]{125*3}=\sqrt[3]{125}*\sqrt[3]{3}=5\sqrt[3]{3}

Hence, the possible values for x in the equation, are:

First option, 5\sqrt[3]{3}

Second option,  \sqrt[3]{375}

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