Question

4 16 18 20 x

Explanation:

Step1: Recognize congruent triangles

Since the two triangles are isosceles right - angled triangles (indicated by the equal sides and right - angle), they are congruent. The ratio of corresponding sides is equal.

Step2: Set up proportion

The ratio of the height to the hypotenuse in the first triangle is the same as in the second triangle. In the first triangle, if the height is 18 and the hypotenuse is 20, and in the second triangle, the height is 16 and the hypotenuse is $x$. We have the proportion $\frac{18}{20}=\frac{16}{x}$.

Step3: Cross - multiply

Cross - multiplying gives us $18x = 16\times20$.

Step4: Solve for $x$

$x=\frac{16\times20}{18}=\frac{320}{18}=\frac{160}{9}\approx17.78$.

Answer:

$\frac{160}{9}$