Guest house is 15m long and 12m wide. what is the diagonal of the house?

The diagonal of the house is approximately 19.21m

Step-by-step explanation:

Taking the shape of the house as a rectangular building, if length l is 15m and width w is 12m, then to find the diagonal, we can relate the shape now formed to a right angle triangle as the diagonal line divides the rectangular house into 2 right angled triangle.

We can now say the diagonal line is d.

To solve the question, we can consider pythagoras theorem which is

+ =

The length l and width w can be taking as opposite and adjacent a and b respectively, while diagonal d can be taking as hypothenus c

+ =

Substitute for length 15m and width 12m, we will have

+ =

225 + 144 =

369 =  

d =

d = 19.2094

d ≈ 19.21m

2.83941151 would be the answer you're looking for! : )

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.