Math Help!!! Solve the isosceles right triangle?

Question

The hypotenuse of an isosceles right triangle is 3 meters longer than either of its legs. Find the length of the legs, and approximate your answer to 2 decimal places.
This problem is unable to be solved by factoring.

Answer 1

x*sqrt(2) = x + 3

sqrt(2) = 1 + 3/x

3/x = sqrt(2) - 1.

x = 3/(sqrt(2) - 1)

Its legs are x, approximately 7.24 meters long.

Answer 2

Do you in worry-free words advise "the circle divides the top into 2 elements contained in the ratio a million : 3"? Why confuse the challenge by skill of apparently evaluating it to the bottom ? the top of an isosceles triangle commonly refers back to the median which bisects the attitude between both equivalent aspects, so the bottom is the unequal aspect. in case you do advise that the top is split contained in the ratio a million : 3 by skill of the circle (which I take to characterize that the diameter of the circle is a million/4 of the top), then the diameter of the circle represents the a million, so its radius = ½, or a million/7 of the top. the gap from the centre of the circle to the vertex of the triangle = 3 + radius of the circle = 3½. Draw a radius from the centre of the circle to the point the position between the aspects of the triangle is tangent to the circle. the attitude between this radius and the aspect of the triangle is a correct attitude. So it varieties a smaller triangle it really is such as the large triangle. the attitude (call it ?) on the centre of the circle between the radius and the median is the same because the bottom attitude (also ?) of the large triangle. From this smaller triangle we get that cos ? = (radius of circle)/(centre to the triangle vertex) = ½ / 3½ = a million/7. From the large triangle, we get that cos ? = (1/2 the bottom / L) = 6 / L (the position L = the dimensions of the aspect of the large triangle, which it truly is had to discover). Equating those 2 expressions, a million/7 = 6/ L, therefore L = 40 2 it truly is, the dimensions of the aspects of the isosceles triangle = 40 2. And the extremely top of the triangle = ?(40 2² - 6²) = ?1728 = 40-one.57, the radius of the circle = 40-one.57/7 = 5.ninety 4

Answer 3

OK.

So if you have an isosceles triangle, two of the three sides are congruent. So this means that the two legs are congruent to each other.

This also means that the base angles of the triangles are congruent. And since the angles in a triangle have to be supplementary and you KNOW that one of the angles is 90...

180-90=90. Divide 90 by 2 (so you can get the measure of the two base angles), and your quotient is 45. Each base angle measures 45 degrees.

Because of this, we have a special right triangle...45-45-90.

The hypotenuse is radical 2 times longer than either leg.



OK, now that we know that...

0.7071 is the square root of two divided by two. Keep that in mind as I give you the equation!



x(radical two)=0.7071(x+3)

Divide each side by the square root of two now.

x=0.7071x+2.1213/1.414

x=(1/2 x) + 2.1213

This means that x=4.2426.



SO EACH LEG EQUALS 4.2426 or 4.24. TA-DA!



Hopefully you understand how I got there!

Answer 4

Make the legs =x



the hypotenuse =3+x



Using the pythag theorem a^2+b^2=c^2 you can solve for x



x^2+x^2=(3+x)^2



2x^2=9+6x+x^2



x^2-6x-9=0



use the quadratic equation to solve this for x

Answer 5

let a leg = x

x^2 + x^2 = (3 + x)^2

2x2 = 9 + 6x + x2

x2 = 9 + 6x

x2 - 6x - 9 = 0

plug this into the quad equation with a =1 , b= -6, c = -9and take the positive answer

Answer 6

email your teacher and ask for help. if someone gives it to you then you wont learn it