The area of a right angled triangle is 30 cm$^2$ and the length of its hypotenuse is 13 cm . the length of the shorter is :

Let the legs be a and b, where b is the shorter side; we have 0.5 times a times b = 30 and a^2 + b^2 = 13^2 = 169. From the area equation, a = 60 divided by b, which we substitute into the Pythagorean theorem to get (60 divided by b)^2 + b^2 = 169. Multiplying by b^2 gives b^4 - 169b^2 + 3600 = 0, which factors to (b^2 - 25)(b^2 - 144) = 0, meaning the shorter side b is 5 cm.

• Thanks
• Wrong explanation