The accompanying diagram SQRE is a square and the diagonals intersect at T. a. ST = 2x + 3, EQ = 6x – 11. Find the length of EQ b. mETS = 3w – z, mERQ = w – 2z Find the values of w and z.

Question

Draw a square and then do it. Please do it as soon as possible.

Answer 1

a) Diagonals of a square bisect so SR = 2 * ST = 4x + 6

Diagonals of a square are equal so SR = EQ:

4x + 6 = 6x - 11

2x = 17

x = 8.5

EQ = 6(8.5) - 11 = 40

b)

In a square diagonals are perpendicular so m<ETS = 90

Also all four interior angles are right angles so m<ERQ = 90

so 3w -z = 90

w - 2z = 90

multiply top row by -2

-6w + 2z = -180

w - 2z = 90

add two rows

-5w = -90

w = 18

w - 2z = 90

18 -2z = 90

-2z = 72

z = -36