Longest side of a triangle is 20 cm and another side is 10 cm If area of the triangle is 80 cm2 then...........

Quantitative Aptitude ( CCS) Geometry

Longest side of a triangle is 20 cm and another side is 10 cm. If area of the triangle is 80 cm², then what is the length (in cm) of its third side?

260

250

256

240

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Explanation:

Let PS be altitude of ΔPQR.
Area of ΔPQR = 80 = 1/2 × QR × PS
⇒ 80 = 1/2 × 20 × PS
⇒ PS = 8 cm
As we know, PQ = 10 cm and PS = 8 cm
Now, by the pythagorean theorem, we get
∴ In ΔPSQ, QS = 6 cm
∴ SR = QR – PS = (20 – 6) = 14 cm
In ΔPSR,
PR2 = PS2 + SR2 = 82 + 142 = 260.
∴ PR = √260 cm