Question

The perimeter of a right angle triangle is 12 and hypotnuse 5 . find area

Answer 1

Let the two legs of the triangle be x and y.

Then x+y+5=12 and x2+y2=52

y=7−x

Substituting:

x2+(7−x)2=25

x2+49−14x+x2=25

2x2−14x+24=0

2(x2−7x+12)=0

2(x−3)(x−4)=0

x=3and4

The two legs measure 3 and 4 cm. The area is given by A=B×H2, where B and H are the two legs.

A=3×42

A=6 square centimetres.

In summary:

The triangle has sides of 3,4and5 centimetres. The area is of 12 cm2