my work is at the end of the ques. but i get the answer wrong?

There are 2 major mistakes.

No way is the coefficient of linear expansion of concrete 7.4e-13 (and you forgot the units!).

A typical value is 1.45e-5 ⁰C⁻¹

And no way is 7.4e-13x2.4x38°=0.0010944 (and you forgot the units!)

It comes to 6.75e-11 m.

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Using 1.45e-5 ⁰C⁻¹ for the coefficient of linear expansion:

Each block expands an amount d:

d = 1.45e-5 ⁰C⁻¹ x 2.4 x 38°= 0.00132m

Call each gap size G. So the total amount of allowed expansion is 2G as there are 2 gaps,

Each block expands by an amount 0.00132m. Since there are 3 blocks:

3 x 0.00132 = 2G

G =(3/2) x 0.00132 = 2.0e-3m (=2mm)

The official answer may be slightly different depending on what value is used for the coefficient of linear expansion of concrete.

If K is the linear expansion coefficient for concrete, it is much too small. It should be on the order of e-6 not e-13. Perhaps you have looked up the wrong data.

Apart from the above mistake, your calculation of the expansion

∆L=7.4e-13x2.4x38°=.0010944

.0010944x(3/2)=.0016416m

uses the correct method, but your arithmetic is wrong, it should be 1.0e-10m.

Your answer should be quoted to 2 sig figs, the same as 2.4. 7.4 and 38.

ΔL=kLΔT

ΔL=7.4e^-13*2.4*38 =1.525 mm

the distance X between the walls is

X=3L+3ΔL

it must be

X=3L+2x

then

gap is

x=3/2ΔL = 2.288 mm