Question

Someone please explain the solution to this :

Answer 1

Answer: 17.5 units.

Step-by-step explanation:

The triangle LAY is a similar triangle to LYW. It has the same angle measures, but different side lengths. The hypotenuse of LAY is the line LY, while the hypotenuse of LYW is the line LW.

We can use the line LY to find LW.

Use the Pythagorean Theorem to find LY:

(3.5)^2 + 7^2 = 61.25

So, LY has a length of $\sqrt{61.25}$.

You can then use proportions to find the distance of LW.

The line LA is the base of the smaller triangle, and the line LY is the base of the larger triangle.

The line LY is the hypotenuse of the smaller triangle, and the line LW is the hypotenuse of the larger triangle.

$\frac{3.5}{\sqrt{61.25} } =\frac{\sqrt{61.25} }{y}$

You can then cross multiply to get this equation:

$61.25 = 3.5y$

So, the line LW has a length of 17.5.