Question

Construct a right triangle whose base is 12 cm and the difference in lengths of its hypotenuse and the other side is 8cm.

Answer 1

Sides of the triangle are

H=13

B=12

L=5

Answer 2

Answer: Let's call the length of the side of the right triangle that is not the base "a". The length of the hypotenuse is "c".

Since the difference between the hypotenuse and this side is 8 cm, we know that:

                                                  c - a = 8

We also know the base of the triangle, which is 12 cm, so we can use the Pythagorean theorem to solve for "a" and "c":

                                             c^2 = a^2 + 12^2

Expanding the right side:

                                            c^2 = a^2 + 144

Now we can substitute the equation from the first equation into the second equation:

                                            c^2 = a^2 + 144

                                            c^2 = (c - 8)^2 + 144

                                            c^2 = c^2 - 16c + 64 + 144

                                               0 = -16c + 208

Solving for c:

                                             16c = 208

                                                 c = 13

So the length of the hypotenuse is 13 cm, and the length of the other side is:

                                             a = c - 8 = 13 - 8 = 5

So the right triangle has a base of 12 cm, the other side has a length of 5 cm and the hypotenuse has a length of 13 cm.

Learn more about the right triangle here

https://brainly.in/question/36234424

Learn more about the Pythagorean theorem here

https://brainly.in/question/2829237#:~:text=Expert%2Dverified%20answer&text=In%20a%20right%20angle%20triangle,two%20sides%20and%20vice%20versa.&text=Pythagoras'%20theorem%3A,the%20other%20two%20perpendicular%20sides.

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