Question

two adjacent sides of a right angled triangle are (2x+2) and 6 cm if the area of the triangle is 30cm^2 find the length of hypotenuse​

Answer 1

Answer:

Area of right angled triangle = $\frac{1}{2}$ X Base X height

               = $\frac{1}{2}$ X Product of two sides of the triangle (Excluding the hypotenuse)

or, 30 $cm^{2}$ =  $\frac{1}{2}$  X (2x + 2) X 6

or, 10 = 2x + 2

or, 8 = 2x

or, x = 4cm

From Pythagorus theorem,

$a^{2} + b^{2} = h^{2}$

where a and b are sides of right-angled triangle and h is hypotenuse

or, $6^{2} +$ $4^{2}$ = $h^{2}$

or, h = $\sqrt{52}$ = 2 $\sqrt{13}$ cm