Answered

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Quiz: Solving Quadratic Equations 6:Quadratic Equations and Functions Х A= 53 sq. in. Find the value of x. If necessary, round to the nearest tenth.

Sagot :

We know that the triangle has an area of 53 sq in.

We also know that the area of any triangle is:

[tex]A=\frac{1}{2}b\cdot h[/tex]

In this case, the base and the height are equal to x. Then:

[tex]A=\frac{1}{2}x\cdot x=\frac{1}{2}x^2[/tex]

And, as we said, the area is 53, this means that:

[tex]\frac{1}{2}x^2=53[/tex]

Solving for x, we have:

[tex]\begin{gathered} \frac{1}{2}x^2=53 \\ x^2=2\cdot53 \\ x^2=106 \\ x=\sqrt[]{106} \\ x=10.3 \end{gathered}[/tex]

Therefore, x=10.3.

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