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# The Hypotenuse of a Right-angled Triangle Exceeds One Side by 1 Cm and the Other Side by 18 Cm; Find the Lengths of the Sides of the Triangle. - ICSE Class 10 - Mathematics

#### Question

The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.

#### Solution

Let one hypotenuse of the triangle be x cm.
From the given information,
Length of one side = (x – 1) cm
Length of other side = (x – 18) cm
Using Pythagoras theorem,
x2 = (x – 1)2 + (x – 18)2
x2 = x2 + 1 – 2x + x2 + 324 – 36x
x2 – 38x + 325 = 0
x2 – 13x – 25x + 325 = 0
x(x – 13) – 25(x – 13) = 0
(x – 13) (x – 25) = 0
x = 13, 25
When x = 13, x – 18 = 13 – 18 = -5, which being negative, is not possible.
So, x = 25
Thus, the lengths of the sides of the triangle are x = 25 cm, (x – 1) = 24 cm and (x – 18) = 7 cm.

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6B | Q: 4

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Solution The Hypotenuse of a Right-angled Triangle Exceeds One Side by 1 Cm and the Other Side by 18 Cm; Find the Lengths of the Sides of the Triangle. Concept: Quadratic Equations.
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