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I need help on 2. The triangle one; finding the perimeter and area. The triangle is scalene if you can’t see it by the way.

I need help on 2. The triangle one; finding the perimeter and area. The triangle is-example-1
User Benjguin
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1 Answer

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Given,

The measure of base of triangle is 20 cm.

The measure of altitude of the triangle is 12 cm.

The expression of area of the triangle is,


A=(1)/(2)* base*\text{altitude}

Substituting the values in the expression then,


\begin{gathered} A=(1)/(2)*20*\text{1}2 \\ A=10*\text{1}2 \\ A=120cm^2 \end{gathered}

The area of the triangle is 120 cm^2.

Consider,

The third side of the triangle is 2x cm.

The semiperimeter of the triangle is,


S=(20+12+2x)/(2)=16+x

Area of triangle,


\begin{gathered} A=\sqrt[]{(16+x)(16+x-12)(16+x-20)(16+x-x)} \\ A=\sqrt[]{(16+x)(x+4)(x-4)16} \\ A=\sqrt[]{(256+16x)(x^2-16)} \\ A=\sqrt[]{256x^2+16x^3-256x-4096} \end{gathered}

Equation both area then,


\begin{gathered} 120=\sqrt[]{16x^3+256x^2-256x-4096} \\ 14400=16x^3+256x^2-256x-4096 \\ (18496)/(16)=x^3+16x^2-16x \\ x^3+16x^2-16x-1156=0 \end{gathered}

After solving this expression, the value of x is 7.38.

The third side of the triangle is,


2x=2*7.38=

User Thomas
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