Mathematics
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Answer
Given,
Hypotenuse = 13 cm
Let base = x cm, so perpendicular = (x - 7) cm.
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ 132 = (x - 7)2 + x2
⇒ 169 = x2 + 49 - 14x + x2
⇒ 169 = 2x2 - 14x + 49
⇒ 2x2 - 14x + 49 - 169 = 0
⇒ 2x2 - 14x - 120 = 0
⇒ 2(x2 - 7x - 60) = 0
⇒ x2 - 7x - 60 = 0
⇒ x2 - 12x + 5x - 60 = 0
⇒ x(x - 12) + 5(x - 12) = 0
⇒ (x + 5)(x - 12) = 0
⇒ x + 5 = 0 or x - 12 = 0
⇒ x = -5 or x = 12.
Since, side cannot be negative.
∴ Base(x) = 12 cm, Altitude (x - 7) = 5 cm.
Hence, other two sides are 5 cm and 12 cm.
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