Question

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.

Answer 1

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=`