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

The diagonals are bisected. All diagonals are equal since SQRE is a square. All half diagonals are equal.

a) ST = 2x+3 = EQ/2 = (6x-11)/2

2x+3 = 6x-11

14 = 4x

x = 14/4 = 7/2

EQ = 6x-11 = 6(7/2)-11 = 21-11 = 10

b) All the angles at point T are 90°. There is probably some geometry theorem that shows that. But, since SQRE is a square, bisected corner angles are 45°. So 45 +45 +x = 180, x = 90.

m∠ETS = 90 = 3w-z

m∠ERQ = 90 = w-2z Since ∠ERQ is a corner of a square.

w = 90+2z

Substitute w into the first equation

90 = 3(90+2z)-z = 270 +6z -z = 270+5z

5z = 90-270 = -180 --> z = -36 and w = 90 + 2(-36) = 18

z = -36 and w = 18

Answer 2

Length of ET = 2 times length of ST...so put the 2 expressions in a equation, solve for x and then evaluate EQ.

For the 2nd part I'm not sure what your notation means. What is m .followed by a square mean?