Question

the sides in cm of a right triangle containing the right angle are 3 (x+1) and 2x-1 . if the area of the right triangle is 30 cm2 , find the sides of the triangle ​

Answer 1

ANSWER:-

Given:

•The sides (in cm) of a right ∆ containing the right angle are 3(x+1) & (2x-1).

•The area of triangle is 30cm²

To find:

The sides of the triangle.

Solution:

We know that, area of triangle is;

=) 1/2 × base × height

$= > \frac{1}{2} \times (2x - 1) \times 3(x + 1) = 30 \\ \\ = > \frac{1}{2} \times (2 {x}^{2} + 2x - x - 1)3 = 30 \\ \\ = > \frac{1}{2} \times 2 {x}^{2} + x - 1 = 10 \\ \\ = > \frac{2 {x}^{2} + x - 1}{2} = 10 \\ \\ = > 2 {x}^{2} + x - 1 = 20 \\ \\ = > 2 {x}^{2} + x - 1 - 20 = 0 \\ \\ = > 2 {x}^{2} + x - 21 = 0 \\ \\ = > 2 {x}^{2} + 7x - 6x - 21 = 0 \\ \\ = > x(2x + 7) - 3(2x + 7) = 0 \\ \\ = > (2x + 7)(x - 3) = 0 \\ \\ = > 2x + 7 = 0 \: \: or \: \: \: x - 3 = 0 \\ \\ = > 2x = - 7 \: \: or \: \: x = 3 \\ \\ = > x = \frac{ - 7}{2} \: \: \: \: \: or \: \: \: \: \: x = 3$

Negative value isn't acceptable & angle is not come negative.

So,

x= 3

•Base = 3(x+1)

=) 3(3+1)

=)3(4)

=) 12cm

•Height= 2x -1

=) 2×3 -1

=) 6 -1

=) 5cm

Thus,

The side of a triangle is 12cm & 5cm.

Thank you.