Question

The triangle PQR is right angled at Q. If PQ =5 cm, QR =12 cm. If QS is perpendicular to PR, then QS in cm is equal to​

Answer 1

Given:-

• In ∆PQR sides are PQ = 5 cm and QR = 12 cm.
• ∆PQR is right angled at Q.

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To find:-

• QS ( Which is perpendicular on side PR).

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$\huge \tt \:☃\: Solution$

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For side PR

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Formula used:-

Pythagoras theorem:-

☘ (Base)² + (Perpendicular)² = (Hypotenuse)²

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Perpendicular = PQ = 5 cm

Base = QR = 12 cm

Hypotenuse = PR = To find

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Put the values in formula

⇒(5)² +(12)² = (PR)²

⇒25 + 144 = (PR)²

⇒169 = (PR)²

⇒√169 = PR

⇒PR = 13

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☘ Area of triangle = $\frac{1}{2}$× Base × height

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Base = 12cm

Height = 5 cm

Put the values

⇒$\frac{1}{2}$× 12 × 5

⇒6 × 5

⇒30 cm²

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Area will be same if we take PR to be base and QS to be Perpendicular.

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PR = 13 cm ( As we find above)

QS = To find

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⇒30 = $\frac{1}{2}$× QS × 13

⇒$\frac{30 × 2}{13}$ = QS

⇒$\frac{60}{13}$ = QS

⇒QS = 4.615 cm.

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Thus, the measure of QS is 4.615 cm.

Answer 2

Step-by-step explanation:

answer is option c 60/13