Question

1. what is the length of the hypotenuse of a right triangle with legs measuring 7 units and 24 units?

a. 16 units
b. 25 units
c. 27 units
d. 25 units

1. if triangle abc is similar to triangle def and the length of ab is 5 units while the length of de is 10 units, what is the scale factor from triangle abc to triangle def?

a. 10
b. 1/2
c. 2
d. 5

1. if a triangle is divided into two smaller triangles by an altitude and all three triangles are similar, what theorem could this be used to prove?

a. sss criterion
b. pythagorean theorem
c. hl criterion
d. sas criterion

1. rectangle r with side lengths 4 and 6 is dilated by a scale factor of 2. what are the side lengths of the resulting rectangle?

a. 2 and 3
b. 6 and 9
c. 8 and 12
d. 10 and 15

1. a ladder leaning against a building creates a right triangle with the ground. the ladder is 20 ft long, and the base of the ladder is 16 ft from the building. how high does the ladder

a. 10 ft
b. 15 ft
c. 11 ft
d. 12 ft

1. which of the following statements is

ot\ true about similar figures?
a. side lengths are proportional.
b. a dilation can create similar figures.
c. corresponding angles are congruent.
d. similar figures must be the same size.

1. a rectangle with vertices p(0, 1), q(4, 1), r(4, 3), and s(0, 3) is translated to p(2, -1), q(6, -1), r(6, 1), and s(2, 1). what is the translation rule?

a. (x + 2, y + 1)
b. (x + 2, y - 1)
c. (x - 2, y + 1)
d. (x - 2, y - 1)

Explanation:

Step1: Use Pythagorean theorem

For a right - triangle with legs \(a = 7\) and \(b = 24\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse.

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=7^{2}=49\), \(b^{2}=24^{2}=576\), then \(a^{2}+b^{2}=49 + 576=625\).

Step3: Find the value of \(c\)

\(c=\sqrt{625}=25\).

Answer:

B. 25 units