Question

The perimeter of a right triangle is 24 cm. If it's hypotenuse is 10cm.Find its area

Answer 1

let the sides be a,b,c
a+b+c=24
hypotenuse=10cm be c
a+10+b=24
a+b=14
b=14-a
using pythagoras theorem,
c²=a²+b²
10²=a²+(14-a)²
100=a²+(196+a²-2.14.a)
100=a²+196+a²-28a
2a²-28a+96=0
2(a²-14a+48)=0
a²-14a+48=0
a²-6a-8a+48=0
a(a-6)-8(a-6)=0
(a-8)(a-6)=0
either a-8=0 or a-6=0
a=8 or a=6
therefore,c=6cm or 8cm (as a+c=14)
now,area of triangle=1/2 × base × height
here base can 8cm and height can be 6cm
1/2×8×4
16cm²