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# 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. - ICSE Class 10 - Mathematics

#### Question

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.

#### Solution

Hypotenuse = 26 cm
The sum of other two sides is 34 cm.
So, let the other two sides be x cm and (34 – x) cm.
Using Pythagoras theorem,
(26)2 = x2 + (34 – x)2
676 = x2 + x2 + 1156 – 68x
2x2 – 68x + 480 = 0
x2 – 34x + 240 = 0
x2 – 10x – 24x + 240 = 0
x(x – 10) – 24(x – 10) = 0
(x – 10) (x – 24) = 0
x = 10, 24
When x = 10, (34 – x) = 24
When x = 24, (34 – x) = 10
Thus, the lengths the three sides of the right-angled triangle are 10 cm, 24 cm and 26 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: 2

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Solution 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. Concept: Quadratic Equations.
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