Question

Thethree sides of a right-angled triangle are x, x+1 and 5. Find x and thearea, if the longest side is 5.

Answer 1

Answer:

For the right triangle,we have three sides x,(x+1)and 5 in which 5 is the longest side as the hypotenuse of the triangle.

Now, we know that I'm a right triangle,the square of the hypotenuse is the sum of the squares of the other two sides.

That is,

(5)²=(x)²+(x+1)²

25=x²+x²+2x+1

25=2x²+2x+1

2(x²+x)=25-1

2(x²+x)=24

(x²+x)=24/2

x²+x= 12

x²+x-12=0

x²+4x-3x-12=0

x(x+4)-3(x+4)=0

(x+4)(x-3)=0

so, x+4=0. and. x-3=0

x=0-4. x=0+3

x=(-4). x=3

Since the value of the x can't be negative in this case ,hence more accurately we take x=3.

hence the 1st side = x = 3m

other side = x+1= 3+1 =4

Now,

Area of the right triangle = 1/2× 3×4

= 6m² Ans.

Answer 2

Step-by-step explanation:

Pythagoras theorem can be used for a right angled triangle which is:-

$hypotenuse {}^{2} = base {}^{2} + prependicular {}^{2}$

where hypotenuse is always a longer side so here hypotenuse = 5

now let us find base and prependicular :–

$x {}^{2} + (x + 1) {}^{2} = 5 {}^{2}$

$x {}^{2} + {x}^{2} + 1 = 25$

$2 {x}^{2} = 25 - 1$

${x}^{2} = 24 \div 2$

${x}^{2} = 12$

$x = \sqrt{12}$