Question

the perimeter of right triangle is 24 cm . if it hypotenus is 10 cm , find the other two sides . find its area by using formula area of the right triangle

Answer 1

Answer:

other two sides of triangle are 6cm and 8 cm

area of triangle = 24cm²

Step-by-step explanation:

Let the other two sides be x and y respectively.

perimeter = sum of sides

24 = x + y + 10....(given)

x + y = 14

Now by Pythagoras theorem,

(hypo)2 = sum squares of remaining two sides

(10)² = x² + y²

i.e. x²+y² = 100

Now,

(x+y)²= x²+2xy+y²

(14)² = 100+2xy

196-100= 2xy

xy= 96/2 =48

area of triangle = 1/2(sides forming right angle)

= 1/2(xy)

= 1/2(48) = 24 cm²

Answer 2

Answer:

24.

let other sides be a,b

Sum of a and b =perimeter-hypotenus

=24-10=14

i.e a=14-b

By pythagorean theorem h^2=a^2+b^2

100=(14-b)^2 +b^2

100=196+b^2 - 2×14×b +b^2

=2b^2- 28b +96

dividing by 2 =b^2-14b +48

by finding factors of 48 that when added gives -14

the factors are -8, -6

So a,b are 8 and 6

Area =1/2×base×height

= 1/2×8×6

=24 square cm.