Question

the side of a triangle containing the right angle are 5x and 3x-1.... if the area of triangle is 60cm^2...find the side of the triangle

Answer 1

YOUR solution:=》

1/2 bh

1/2 (5x (3x-1)) = 60

1/2 (15x^2 -5x ) = 60

15x^2 - 5x = 120

15x^2 -5x - 120 = 0

3x^2 - x - 24 = 0

3x^2 + 8x - 9x - 24 = 0

x(3x + 8) -3 (3x + 8)

(x-3) (3x + 8)

x = 3 or x = -8/3

since length cannot be -ve

x = 3


so the sides of the triangle are

5(3) and 3(3) - 1

15 and 8

Pythogorean prop

8^2 + 15^2 = hypotenuse ^2

(sum of the squares on the two non - hypotenuse sides is equal to the square on the hypotenuse )

64 + 225 = 289

hypotenuse sqr = 289
hy[otenuse = Route of 289

Hyp - 17 !!

Answer 2

$given \: \frac{1}{2} \times 5x \times (3x - 1) = 60 \\ x(3x - 1) = 12 \\ 3 {x}^{2} - x - 24 = 0 \\ using \: standard \: formula$
$x = 3 \: or \: - \frac{8}{3} \\ taking \: positive \: value \: sides \: are \\ 5 \times 3 = 15 \: and \: 3 \times 3 - 1 = 8$