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The Sides of a Right-angled Triangle Are (X – 1) Cm, 3x Cm and (3x + 1) Cm. Find: (1) the Value of X, (2) the Lengths of Its Sides, (3) Its Area. - ICSE Class 10 - Mathematics

Question

The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:

(1) the value of x,
(2) the lengths of its sides,
(3) its area.

Solution

Longer side = Hypotenuse = (3x + 1) cm
Lengths of other two sides are (x – 1) cm and 3x cm.
Using Pythagoras theorem,
(3x + 1)2 = (x – 1)2 + (3x)2
9x2 + 1 + 6x = x2 + 1 – 2x + 9x2
x2 – 8x = 0
x(x – 8) = 0
x = 0, 8
But, if x = 0, then one side = 3x = 0, which is not possible.
So, x = 8
Thus, the lengths of the sides of the triangle are (x – 1) cm = 7 cm, 3x cm = 24 cm and (3x + 1) cm = 25 cm.
Area of the triangle = ½ × 7 cm × 24 cm = 84 cm²

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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: 3

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Solution The Sides of a Right-angled Triangle Are (X – 1) Cm, 3x Cm and (3x + 1) Cm. Find: (1) the Value of X, (2) the Lengths of Its Sides, (3) Its Area. Concept: Quadratic Equations.
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