Mathematics
The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.
Answer
Let the length of perpendicular be x cm so base = (34 - x) cm.
We know that,
⇒ (Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ (26)2 = (x)2 + (34 - x)2
⇒ 676 = x2 + 1156 + x2 - 68x
⇒ 2x2 - 68x + 1156 - 676 = 0
⇒ 2x2 - 68x + 480 = 0
⇒ 2(x2 - 34x + 240) = 0
⇒ x2 - 34x + 240 = 0
⇒ x2 - 24x - 10x + 240 = 0
⇒ x(x - 24) - 10(x - 24) = 0
⇒ (x - 10)(x - 24) = 0
⇒ x - 10 = 0 or x - 24 = 0
⇒ x = 10 or x = 24.
Hence, length of the sides of triangle are 10 cm, 24 cm and 26 cm.
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