Question

the sides of a right angled triangle is x plus 1 and x plus 3 and length of its hypotenuse is 10cm find the area of the triangle​

Answer 1

Vanadium is 3 rd transition metal . It show hard, malleable , ductility properties .it is form wire . It is present in earth curst in the form of rock oil, iron rock and phosphorous rock .it show anti corrosion properties . It is 1st element present in 5 th group . It is rarely found earth metal

Discovery : vanadium is discovered by 2 times First time it is discovered in 1801 by scientist Andres maueldel Raw in Mexico City Second time it is discovered by scientists Nil Gabrief selfstrom in 1830. He was found vanadium element from iron made ore it is an oxide form

Origin of name :. The name vanadium is derived from word ‘ vandis’

The meaning of this word is goodness beauty . I.e. Multi colour chemical element

Physical properties :

1) Atomic symbol: vanadium is denoted by symbol V

2) Atomic number : atomic number of vanadium is 23 In vanadium 23 proton and 23 electron is present

3) Atomic weight/ mass: atomic weight of vanadium is 50.94 amu In vanadium atom nucleus 23 proton, 28 neutron is present Sum of proton and neutrons gives atomic mass

4) Position :. It is place in 4th row ( period) and 5th column ( group ) It is 5 th group element

5) Block : it is place in d block

6) Colour : it is silver colour element

7) Odour : it is odourless metal

8) Nature :. It is found in nature at solid state

9) Boiling point : boiling point of vanadium is 34070 C

10) Melting point : melting point of vanadium is 19100 C

11) Isotopes: Vanadium show 2 stable isotope

50V: atomic weight of this isotope is 49.9 amu In this isotope 23 proton ,23 electron and 28 neutron is present. It is present 0.25% present

51V: Atomic weight of this isotope is 50.9 amu

In This isotope 23 proton,23 neutron and 28 neutron is present It is present 99.7% Other 3 radio active isotopes is present 48V ,49V, 52V

Answer 2

Answer:

ok

Explanation-

Let the perpendicular side be 'p', the base side be 'b' and the hypotenuse be 'h'

Then, according to Pythagoras theorem,

$h^{2} = p^{2} + b^{2}$

h = 10cm , let 'b' be x+1 and 'p' be x+3

then, according to the formula,

$(10)^{2} = (x+3)^{2} + (x+1)^{2}$

Now , there is a formula to calculate this.

this is  -   $(a+b)^{2}=a^{2}+ 2ab + b^{2}$

using this formula, we get

$100 = [x^{2} + 2 * x* 3 + (3)^{2}] + [ x^{2} + 2 * x * 1 + (1)^{2}]$

$100 = x^{2} +6x + 9 + x^{2} + 2x + 1$

$100 = 2x^{2} + 8x + 10$

$100 - 10 = 100 = 2x^{2} + 8x$

$90 = 2x^{2} + 8x$

$2x^{2} + 8x -90 = 0$

now, by using the splitting method, we get

[ just to make you sure, in this method we have to find such to numbers, with which when we add them, we  should get 8x, and when we multiply them, we should get $2x^{2} *( -90) = -180x^{2}$ ]

Such two numbers are 18x and -10x

hence,

$2x^{2} + 18x - 10x - 90 = 0$

Taking 2x and -10 common,

$2x(x+9) - 10(x + 9)$= 0$(x+9)(2x-10) = 0$

now taking x+9 common

$(x+9)(2x-10) = 0$

now x is either (-9) or 10/2= 5.  [we transposed first 9 and then -10/2 to RHS]

These are the two values of 'b' and 'p'

hence, b = x + 1 = (9) + 1 = 10 and p = x+3 = 5+3 = 8 [ the lenght cannot be negative]

Now the area of the triangle is = 1/2 * base * hieght [here hieght is perpendicular as it is 90 degree]

hence , area = $\frac{1 * 8 * 8}{2} = \frac{64}{2} = 32m^{2}$

PLZ , for the work i have done for you, mark me as the brainliest