Find the value of x and y that make these triangles congruent by hl.

 the correct option is (A) x = y = 2.

Step-by-step explanation:  We are given to find the values of x and y that makes the triangles in the figure congruent by HL.

From the figure, we note that

triangles ABC and AED are right-angled triangles with hypotenuse AC, AD and one congruent side BC, ED.

Also, AC = 2x + 3, AD = 3y+1, BC = x  and  ED = y.

Since the triangles are congruent by HL postulate, so we must have

Substituting the value of x from equation (i) in equation (ii), we get

So, from equation (i), we arrive at

x = y = 2.

Thus, the correct option is (A).

Fabric (square meters)                   Cloaks

7                                                          21

                                                        4

Step by step explanation:

We are told that Harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. First of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

We can see that 3 cloaks can be made from 1 square meter of fabric. Now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

Therefore, Harry will make 21 cloaks from 7 square meters of fabric.

2. Let us find how many square meters of fabric will be needed to make 4 cloaks.

First of all we will find fabric needed for 1 cloak by dividing 2 by 6.

We can see that fabric needed for 1 cloak is square meter. Now we will multiply by 4 to find fabric needed for 4 cloaks.

Therefore, Harry will need square meters of fabric to make 4 cloaks.