Question

Find the value of x using the diagram below. Round to the nearest whole number. Picture Attached.

Answer 1

so
remember pythagorean therem
if the legs are length a and b and the hyptonuse is c then
a²+b²=c²

also, special right triangle
in 45-45-90 triangle (the inside angle measures are 45 deg, 45 deg, 90 deg, )
if the 2 legs are x then the hytponuse is x√2



so


see the 45 45 90 triangle first
it is a leg of 14
so the hytponuse is 14√2
which is the leg of the larger right triangle


so
te larger one
one leg is 25
the other is 14√2
the hytponuse is x
so

25²+(14√2)²=x²
625+392=x²
1017=x²
sqrt both sides
31.890437438203948223997365744788=x
round
32=x
so 2nd option

Answer 2

both triangles are right triangles. x is the hypotenuse of the upper one. ThePythagorean formula will give the value of x. One side is known, The other side we will find using the fact that the lower right triangle is isosceles. The hypotenuse of an isosceles right triangle has a length of
`√(2)` times the length of one of the legs. In this case 14. So the hypotenuse of the lower triangle is also the short side of the upper triangle. Using Pythagoras


`25^(2) + (14 √(2)) ^(2) = x^(2)`


`625 + 392 = x^(2)`


`1017 = x^(2)`


`32 = x`