l_1/a=a/l_2
In this question we are given the lengths of the segments of the hypotenuse.
l_1=2 and l_2=8
Let's substitute these values and use the Cross Products Property to rearrange the equation.
2/a=a/8
⇓
a^2=2* 8
We get the length of the altitude when we calculate the product and then take the square root.
b Let's make an accurate drawing of the right triangle with the measurements given in Part A.
The process of drawing this triangle is explained in Part C.
c To make our above triangle, we can start with drawing the hypotenuse first and marking the foot of the altitude to the hypotenuse. According to the measurements given in Part A, the hypotenuse is 2+8=10 cm long and the foot of the altitude is 2 cm away from one of the endpoints.
The next step is to use a protractor to measure a right angle to find the line of the altitude.
According to the calculation in Part A, the length of the altitude is 4 cm. Let's use this length to mark the position of the third vertex on the line we drew in the previous step.
Finally, let's connect this third vertex with the endpoints of the hypotenuse.
