Question

The hypotenuse of a right angled is 25 CM if the sum of the other two sides is 31 CM find the other two sides .

Answer 1

Answer:

x=7cm

And, y=24cm.

Step-by-step explanation:

Side be x and y.

$\sqrt{x {}^{2} + y {}^{2} } = 25$

So, x²+y²=625

And, x+y=31

So, x²+y²+2xy=31²

or, 625+2xy=961

or, 2xy=336

or, xy=168

Again, x+y=31

or x=31-y

So, xy=168

or,( 31-y)y=168

or, 31y-y²=168

or, y²-31y+168=0

$y = 31 + \sqrt{ {31}^{2} - 168 \times 4 \ } \div 2$

y=17+31/2=48/2

or, y=24cm

And, x=7cm.

Answer 2

Step-by-step explanation:

Let, Base be 'x'

perpendicular be 'y'

We know that,

x+y=31 CM

x= 31-y cm

Using Pythagoras theorem,

25² = (31-y)² + y²

625 = 961 + y² - 62y +y²

625 - 961 = 2y² -62y

-336 = 2(y² - 31y)

-336/2 = y² - 31y

y² - 31y + 168 = 0

y² -24y - 7y + 168 = 0

y(y-24) -7(y-24) =0

(y-7) (y-24) =0

y-7=0 y-24=0

y= 7 y = 24

Perpendicular = 7cm or 24 cm

x=31-y

x= 31 - 7 or 31-24

x= 24 or 7

Base = 7cm or 24 cm

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