Question

The perimeter of a right triangle is 30cm. Its hypotenuse is 13 cm and base is 5cm. Find

the area of the triangle.The perimeter of a right triangle is 30cm. Its hypotenuse is 13 cm and base is 5cm. Find

the area of the triangle.​

Answer 1

Answer:

30cmsq.

let the 1 side =a=13cm,2side=b=5cm and 3side c=x cm

therefore perimeter of triangle = a+b+c

30=13+5+x

18+x=30

x=30-18

height=c=x=12cm

therefore area of triangle = 1/2xbasexheight

=1/2x5x12

=5x6

=30cmsq.

It may help you

Answer 2

It is given that

ABC is a right angled triangle

BC = 12 cm and AB = 13 cm

Using the Pythagoras theorem

AB2 = AC2 + BC2

Substituting the values

132 = AC2 + 122

By further calculation

AC2 = 132 – 122

So we get

AC2 = 169 – 144 = 25

AC = √25 = 5 cm

We know that

Area of triangle ABC = ½ × base × height

Substituting the values

= ½ × 12 × 5

= 30 cm2

Similarly

Perimeter of triangle ABC = AB + BC + CA

Substituting the values

= 13 + 12 + 5

= 30 cm