Question

Find the value of x. 5 cm 6 cm and x cm

Answer 1

`\sqrt[]{14}`

Step-by-step explanation:

From the figure above, we can see that AB and CD are equal, so y = 5cm.

Let's go ahead and find h using Pythagorean theorem;

`\begin{gathered} 6^2=y^2+h^2 \\ 6^2=5^2+h^2 \\ 36=25+h^2 \\ h^2=36-25 \\ \therefore h=\sqrt[]{11} \end{gathered}`

Since we know h now, let's go ahead and solve for x by applying same Pythagorean theorem on triangle ABC;

`\begin{gathered} 5^2=h^2+x^2 \\ 25=(\sqrt[]{11})^2+x^2 \\ 25=11+x^2 \\ 25-11=x^2 \\ 14=x^2 \\ \therefore x=\sqrt[]{14} \end{gathered}`