geometry questions

[kamranalam81]

Q ) The ratio of the sides of triangle are 2:3:5 and the length of largest side is 52. What is the area of triangle?

Q) The circle lies at the origin of the x- plane with the radius 5. Line K is tangent to circle at [-(2^1/2), (2^1/2)]. find the y-intercept of the line K.

[yoda_ngen]

For question 2, the line is not tangent because the distance from origin to the point (-sqrt(2), sqrt(2)) is not equal to 5 (radius of the circle).

[kamranalam81]

For question 2, the line is not tangent because the distance from origin to the point (-sqrt(2), sqrt(2)) is not equal to 5 (radius of the circle).

instead of using radius 5, use the radius appropriate to question. I cant recall the exact radius.Just want to know the right approach

[dv_dheeraj]

for q 1 sum of 2 sides equals third hence no such tri is possible

[kamranalam81]

for q 1 sum of 2 sides equals third hence no such tri is possible

and what would be the solution if we change the ratio to
2:4:5. Can u please explain?

[Ankost]

Q2. the y -intercept (0, 4*sq.root 2)
Radius = 4, but it doesn't matter here.
y=mx+c, where m- slope, c - y-intercept.
Slope of the tangent line m=1
y-2*sq.root2=1*(x-(-2*sq.root2)
y=x+4*sq.root2
c=4*sq. root 2

[kamranalam81]

Thank you very much Ankost..

[dv_dheeraj]

5x=52 find all three sides of tri find semi perimeter and then the area using semiperimeter formula
A=sqrt(s(s-a)(s-b)(s-c))

[Raj1972]

For Q1) can we do like this
Let a, b,c be 3 sides
5x = 52 , find out x , ==> c (big side)
find a, b using 2:4:5 ratio

TO find out area of Triangle we need b & h
To calculate h make this triangle as two 90 degree triangles
using pythgress theorem find out h
then use the formula .5bh

[DrFrankNFurter]

Q1.
If the ratio of the sides were 3:4:5, a straight approach can be used, as it would be a right triangle. Otherwise, use the semiperimeter formula, but IMHO it takes more than 2 minutes.