7) If in AXYZ, P and Q are two points on XY and XZ respectively such that XP = 4...

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FRYNCZHESTRICXIECATE @FRYNCZHESTRICXIECATE

September 2022 2 1 Report

7) If in AXYZ, P and Q are two points on XY and XZ respectively such that XP = 4 cm
PY = 3 cm, XQ = 6 cm. Find the value of QZ.

A. 3.5 cm
B. 4 cm
C. 4.5 cm
D. 5cm

Jinjinjjara

Verified answer

Question:

If in ∆XYZ, P and Q are two points on XY and XZ respectively such that XP = 4 cm, PY = 3 cm, XQ = 6 cm. Find the value of QZ.

Answer:

C. 4.5 cm

Step-by-step explanation:

$\boxed{ \begin{array}{c}\sf{}XP:PY = XQ:QZ \\ \\ \sf{} 4 : 3 = 6 :x \\ \\ \sf{}\dfrac{4}{3} = \dfrac{6}{ x } \\ \\ \sf{}(4)(x) = (6)(3) \\ \\ \sf{}4x = 18 \\ \\ \sf{}x = \dfrac{18}{4} \\ \\ \boxed{\sf{} x = 4.5} \end{array}} \\ \\$