Question

Find the length of both of the unknown sides in the triangle shown here.

Answer 1

Answer:

$(x+11)^2 = (x+3)^2 +16^2$

And if we solve this equation for x we got:

$x^2 +22x +121 = x^2 +6x +9 +256$

We can cancel $x^2$ in both sides and we have this:

$22x -6x= 256+9-121 =144$

And then we got:

$16 x= 144$

$x =\frac{144}{16}= 9$

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Step-by-step explanation:

For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:

$(x+11)^2 = (x+3)^2 +16^2$

And if we solve this equation for x we got:

$x^2 +22x +121 = x^2 +6x +9 +256$

We can cancel $x^2$ in both sides and we have this:

$22x -6x= 256+9-121 =144$

And then we got:

$16 x= 144$

$x =\frac{144}{16}= 9$

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m