The side of a right angled triangle containing the right angle are 4x cm and (2x-1) cm If the - Maths -

Question

The side of a right angled triangle containing the right angle
are 4x cm and (2x-1) cm If the area of the triangle is 30
cm2 calculate the length of its sides

Ankush Jain · Accepted Answer

Let the base of the triangle be 4x cm

and perpendicular of the triangle be (2x – 1) cm.

Given, area of triangle = 30 cm²

We know that,

Area of triangle = $\frac{1}{2}$ × base × perpendicular (or height)

$\Rightarrow 30 = \frac{1}{2} \times 4 x \times (2 x - 1) \Rightarrow 2 x \times (2 x - 1) = 30 \Rightarrow 2 x^{2} - x - 15 = 0 \Rightarrow 2 x^{2} - 6 x + 5 x - 15 = 0 \Rightarrow 2 x (x - 3) + 5 (x - 3) = 0 \Rightarrow (2 x + 5) (x - 3) = 0 \Rightarrow x = \frac{- 5}{2} and x = 3$

Now, x ≠ $\frac{- 5}{2}$

∴ x = 3 implies that base of triangle = 4x

= 4 × 3

= 12 cm

and perpendicular of the triangle = 2x – 1

= 2 × 3 – 1

= 5 cm

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The side of a right angled triangle containing the right angle are 4x cm and (2x-1) cm. If the area of the triangle is 30 cm2. calculate the length of its sides.

The side of a right angled triangle containing the right angle are 4x cm and (2x-1) cm. If the area of the triangle is 30 cm². calculate the length of its sides.