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प्रश्न
In the following figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is ______.
पर्याय
6 cm
9 cm
4 cm
2 cm
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उत्तर
In the following figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is 4 cm.
Explanation:
Given that, PR = 12 cm, QR = 6 cm and PL = 8 cm
Now, In right angled ΔPLR, using Pythagoras theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ PR2 = PL2 + LR2
⇒ LR2 = PR2 – PL2 = (12)2 – (8)2
⇒ LR2 = 144 – 64 = 80
⇒ LR = `sqrt(80) = 4sqrt(5)` cm
∵ LR = LQ + QR
⇒ LQ = LR – QR = `(4sqrt(5) - 6)` cm
Now, area of ΔPLR,
`A_1 = 1/2 xx LR xx PL`
= `1/2 xx (4sqrt(5)) xx 8`
= `16sqrt(5)` cm2
Again, area of ΔPLQ,
`A_2 = 1/2 xx LQ xx PL`
= `1/2 xx (4sqrt(5) - 6) xx 8`
= `(16sqrt(5) - 24)` cm2
∴ Area of ΔPLR = Area of ΔPLQ + Area of ΔPQR
⇒ `16sqrt(5) = (16sqrt(5) - 24)` + Area of ΔPQR
⇒ Area of ΔPQR = 24 cm2
⇒ `1/2 xx PR xx QM = 24`
⇒ `1/2 xx 12 xx QM = 24`
∴ QM = 4 cm
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