Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.

Given = 8 cm

Answer 1

Remember that

An isosceles triangle has two equal sides

In this problem

we have an isosceles right triangle

that means

the measures of the interior angles are 45-90-45 degrees

the length sides of the legs (perpendicular sides) are equal

see the figure below to better understand the problem

Applying the Pythagorean Theorem

`\begin{gathered} 8^2=a^2+a^2 \\ 8^2=2a^2 \\ 2a^2=64 \\ a^2=32 \\ a=√(32) \\ simplify \\ a=4√(2)\text{ cm} \end{gathered}`