Question

the right triangle pqr is shown. if the dimensions of δpqr are multiplied by a scale factor of 3 to create δpqr, which statement is true?

image of right triangle pqr with right angle at r, qr = 4\, pq = 8\, angle at q is 60°

• the measure of ∠q is 120°.
• the hypotenuse of δpqr has a measure of 24\
• the measure of ∠p is 60°.
• δpqr contains sides with length 6\, 10\, and 12\

Explanation:

Step1: Recall properties of scaling

Scaling preserves angles; sides multiply by scale factor.

Step2: Analyze angle Q'

Original ∠Q = 60°, so ∠Q' = 60° (not 120°).

Step3: Check hypotenuse of P'Q'R'

Original hypotenuse PQ = 8", scaled hypotenuse = 8×3 = 24".

Step4: Analyze angle P'

Original ∠P = 30° (since right triangle, 90+60+30=180), so ∠P' = 30° (not 60°).

Step5: Check scaled sides

Original sides: RQ=4", PR=4√3", PQ=8". Scaled sides: 12", 12√3", 24" (not 6,10,12).

Answer:

The hypotenuse of △P'Q'R' has a measure of 24"