Question

what are the lenghths of the legs in the triangle?give your answer in simplest radical form or rounded to the nearest hundredth.

Answer 1

Here, we are given a 45°-45°-90° triangle.

Let's find the length of the legs.

A 45°-45°-90° triangle is an isosceles triangle, and the two legs of an isosceles triangle are of equal lengths.

To find the length of each leg apply the formula:

`c=a\sqrt[]{2}`

Where;

c = 12

Thus, we have:

`12=a\sqrt[]{2}`

Solve for a:

Divide both sides by √2

`\begin{gathered} \frac{12}{\sqrt[]{2}}=\frac{a\sqrt[]{2}}{\sqrt[]{2}} \\ \\ \frac{12}{\sqrt[]{2}}=a \\ \\ a=\frac{12}{\sqrt[]{2}} \\ \\ \text{Simplify the denominator:} \\ a=\frac{12}{\sqrt[]{2}}\ast\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ \\ a=\frac{12\sqrt[]{2}}{2} \\ \\ a=6\sqrt[]{2} \end{gathered}`

Therefore, the length of each leg in radical form is 6√2

ANSWER:

`6\text{ }\sqrt[]{2}`