Answer:
3) 25
4) 32
Explanation:
In each of the pairs of similar figures, you want to solve for the variable.
3) Right triangles
Sometimes, the problem statement gives you more information than you need. Here, the smaller triangle can be ignored. It has no marking corresponding to x, and the larger triangle has all the information needed.
The Pythagorean theorem can be used to find the length of the hypotenuse, given the lengths of the other two sides in the right triangle.
c² = a² +b²
x² = 15² +20² = 225 +400 = 625
x = √625 = 25
The value of x is 25.
4) Rectangles
The similarity statement ABCD ~ EFGH means we can write the proportion ...
HE/DA = EF/AB . . . . . . . . corresponding sides are proportional
x/28 = 16/14 . . . . . . . . . use the given measures
x = 28(16/14) = 32 . . . . multiply by 28
The value of x is 32.
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Additional comment
If you recognize the ratios of the sides of the right triangles are 15:20 = 3:4, then you can make use of your knowledge of the 3-4-5 right triangle to write the proportion ...
3 : 4 : 5 = 15 : 20 : 25 = 15 : 20 : x ⇒ x=25