If an Isosceles right triangle has an hypotenuse of the square root of 30, what is the length of the other two sides?

For a right angled triangle, hypotenuse is equal to the root of the sum of the squares of the other two sides.

If the sides are ‘a’ and ‘b’ and the hypotenuse is ‘c’,

c = Square Root of (’a’ squared + ’b’ squared)

So, ‘c’ squared = ‘a’ squared + ‘b’ squared.

In the instant case, the triangle is a right angled isosceles triangle; as such the sides are equal, say ‘a’. Also it is given that the square of the hypotenuse is 98.

As such 98 = ‘a’ squared + ‘a’ squared, i.e 2 ‘a’ sq.

So ‘a’ squared = 98/2 = 49

Then ‘a‘ = Root of 49 = 7

ok

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be