The base of a right angled triangle is 12 cm and its hypotenuse is 13 cm long. Find its area and the perimeter.

It is given that,

ABC is a right angled triangle.

From figure,

BC = 12 cm and AC = 13 cm

Using the Pythagoras theorem,

AC² = AB² + BC²

Substituting the values we get,

⇒ 13² = AB² + 12²

⇒ AB² = 13² – 12²

⇒ AB² = 169 – 144 = 25

⇒ AB = $\sqrt{25}$ = 5 cm.

We know that,

Area of triangle ABC = $\dfrac{1}{2}$ × base × height.

Substituting the values we get,

A = $\dfrac{1}{2} \times 12 \times 5$ = 30 cm².

Perimeter of triangle ABC (P) = AB + BC + CA

Substituting the values we get,

= 5 + 12 + 13

= 30 cm.

Hence, area of triangle = 30 cm² and perimeter = 30 cm.