Question

The sides of a triangle are x, x+1, 2x-1 and its area is x root 10 .What is the value of x?

Answer 1

So if the sides = x>-2

Then the area would be that ^10 right?

Answer 2

cn u xplain??

Answer 3

Heron's formula is work
area = sqrt(s(s-a)(s-b)(s-c))

with s = (perimeter of triangle)/2
a,b,c are the sides triangle

Answer 4

first, determine the perimeter of that triangle
perimeter = a + b + c = x + x+1 + 2x - 1 = 4x
so, s = perimeter/2 = 4x/2 = 2x

Answer 5

now, use the Heron's formula above
area = sqrt(s(s-a)(s-b)(s-c))
known area of that triangle is xsqrt(10), so we have the equation
sqrt(s(s-a)(s-b)(s-c)) = x sqrt(10)

Answer 6

distribute the values of s = 2x, a = x, b = x+1, and c = 2x -1 into equation above :
sqrt(s(s-a)(s-b)(s-c)) = x sqrt(10)
sqrt(2x(2x- x)(2x - (x+1))(2x - (2x-1)) = x sqrt(10)
simplify, we get
sqrt(2x * x * (x-1) * 1) = x sqrt(10)
sqrt(x^2 * 2(x-1)) = x sqrt(10)
sqrt(x^2) * sqrt(2(x-1)) = x sqrt(10)
x sqrt(2(x-1)) = x sqrt(10)

Answer 7

just take identicaly, the value in radical must be same. so
2(x-1) = 10
divided by 2 on both sides, we get
x-1 = 10/2
x-1 = 5
add by 1 to both sides, get
x = 5 + 1 = 6

Answer 8

does that make sense, @juhaINA ?

Answer 9

yah..!!:)

Answer 10

ok, glad can help you :)

Answer 11

i hv a question.

Answer 12

what is that ?

Answer 13

in d formula:s-a,s-b,s-c.v don hv to do dat in this question?

Answer 14

well it is already be clear for you, right.
this site might useful :)
http://www.mathsisfun.com/geometry/herons-formula.html

Answer 15

k..thnx

Answer 16

you're welcome