Question

Q7) please answer step by step

Answer 1

Let x , y side of triangle and h(hypotenuse)_

x + y + h(hypotenuse) =60
X+y = 60-25=35

It is right triangle

So, x² + y² = (hypotenuse)²
x² + y²=(25)²=625
Now,
=>(X+y )²=x² + y²+2xy
=>(35)²=625+2xy
=>1225-625=2xy
=>xy=600/2=300

Area of triangle = 1/2 .base.height
Area of triangle = 1/2×xy=1/2×300=150cm²

Answer 2

Given :

In right ∠d Δ ,

Perimeter = 60 cm

Hypotenuse = 25 cm

Let the other sides be a , b and hypotenuse be c

By Pythagoras theorem :

a² + b² = c²

==> a² + b² = ( 25 )²

==> a² + b² = 625 ....................(1)

Perimeter = a + b + c

==> a + b + c = 60

==> a + b + 25 = 60

==> a + b = 60 -25

==> a + b = 35

==> a = 35 - b .......................(2)

Put this in (1) :

(35 - b )² + b² = 625

==> 1225 + b² - 70 b + b² = 625

==> 2 b² - 70 b +600 = 0

==> b² - 35 b + 300 = 0

==> b² - 15 b - 20 b + 300 = 0

==> b ( b - 15 ) - 20 ( b - 20 ) = 0

==> ( b - 15 )( b - 20 ) = 0

Either b - 15 = 0 ==> b = 15

or , b - 20 = 0 ==> b = 20

sides = 20 , 15

Area = 1/2 × 20 cm × 15 cm

        = 150 cm²

Area = 150 cm²

Hope it helps :)

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