What is the value of x?
12 units, 15 units, 20 units, 24 units

Solution:

Given, ST = 9, TQ = 16 and RQ = x 

From similar triangles,

Δ SRQ ⩭ Δ STR ------(1)

{∵ RT 丄 Hypotenuse SQ}

Δ SRQ ⩭ Δ RTQ ------(2)

{∵ Δ SRQ, Δ STR and Δ RTQ are similar triangles}

⇒ SR/ST = SQ/SR = RQ/TR

⇒ SR/9 = 25/SR = x/TR

⇒ SR² = 25 × 9

⇒ SR = 5 × 3 = 15

SR² + RQ² = SQ²

RQ² = SQ² - SR²

RQ² = 25² - 15²

RQ = x = √(625 - 225) = √400

x = 20 units.

Option (iii) is the answer.

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What is the value of x?

Summary:

The value of x in the given figure is 20 units.