Find the diagonal of a square whose sides are of the given measure.

given = 7 square root of 3

The answer is:  " 7√6 units " ; or, write as:  " 17.146 units " .

In this case, a square, the two sides of the square (forming a right triangle) are equal), and the "diagonal" is the hypotenuse of the right triangle.

In these cases, the measurements of the angles of the right triangle are "45, 45, 90" ; and the measurements of the sides are:  "a, a, a√2" ; in which "a√2" is the hypotenuse.

We are given:  "a = side length of the square = 7√3" ;  so, the sides are:
  a, a, a√2 ;  or, "7√3, 7√3, {7√3√2} ;  We are asked to find the diagonal, or hypotenuse;  which is:  "{7√3√2}" ; 

          which is: " 7√6 units "; or, write as:  " 17.146 units " .

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.