Question

If the length of hypotenuse of a right angled triangle is 5cm and its area is 6sq.cm the length of the remaining sides?

Answer 1

3 cm and 4cm

Explanation:

Given that the hypotenuse of a right triangle is 5 cm.

Let the lengths of other two sides of right triangles be `xandy` cm

So `x^2+y^2=25`

Again its area is `6cm^2`

So `1/2xy=6`

`=>xy=12`

Now `(x-y)^2=x^2+y^2-2xy`

So `(x-y)^2=25-24=1`

`x-y=1... (1)`

`(x+y)^2=x^2+y^2+2xy=25+24=49`

`x+y=7......(2)`

Adding (1) and (2)

`2x=8`

`=>x=4`cm

So `y=7-4=3`cm

Answer 2

`3` cm and `4` cm

Explanation:

Here, In a right angled triangle with sides `a,b,` and `c`
`c^2=a^2+b^2`

`a^2+b^2=5^2`
`a^2+b^2=25` ------- eqn 1

By formula,
`1/2 xx axxb=6`
`ab=12`
`b=12/a` ------- eqn 2

Putting value of b from eqn 2 in eqn 1; we get,
`a^2+(12/a)^2=25`
`a^2+144/a^2=25`
`a^4+144=25a^2`
`a^4-25a^2+144=0`
`a^4-16a^2-9a^2+144=0`
`a^2(a^2-16)-9(a^2-16)=0`
`(a^2-16)(a^2-9)=0`
By zero product rule,
Either, `a=4` Or, `a=3`
If `a=4, b=3` And if `a=3, b=4`

So, the remaining sides are `3` cm and `4` cm.

Hope this helps :)

Answer 3

If a question says "the hypotenuse is `5`" there's a pretty good chance the legs will be `3` and `4` because everybody's favorite Pythagorean Triple is `3^2+4^2=5^2.` We check that indeed `1/2 (3)(4) = 6` and we're done.