Using Heron's formula find the area of a right triangle in which the sides containing the right angle measures 20 cm and 15
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Answered by
28
Step-by-step explanation:
It is given that the right angle is formed by the sides measuring 20 cm and 15 cm.
Therefore, let perpendicular = 20cm
Base = 15 cm
Using Pythagoras Therom,
Perpendicular² + Base² = Hypotenuse ²
(20)² + (15)² = Hypotenuse ²
Hypotenuse² = 625
Hypotenuse = 25 cm
Thus, we now know the third side, Hypotenuse = 25.
Semi perimeter = (15 + 20 + 25)/2
= 30 cm
Using Heron's formula,
Area = √[30(30 - 15)(30 - 20)(30 - 25)]
= √[30 × 15 × 10 × 5]
= √[2×3×5 × 3×5 × 2×5 × 5]
= 2 × 3 × 5²
= 150cm²
Thus, area = 150cm²
Hope it helps!
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Answered by
46
Assumption
∆PQR (Right angled triangle)
PQ = c = 20cm
QR = a = 15cm
PR = √{(PQ)² + (QR)²}
PR = √{(20)² + (15)²}
PR = √(400 + 225)
PR = √625
PR = 25 cm
Also here,
s = 30 cm
= 15 × 2 × 5 cm²
= 150 cm²
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