<h2>
Answer:</h2>
The ratio of the area of region R to the area of region S is:

<h2>
Step-by-step explanation:</h2>
The sides of R are in the ratio : 2:3
Let the length of R be: 2x
and the width of R be: 3x
i.e. The perimeter of R is given by:

( Since, the perimeter of a rectangle with length L and breadth or width B is given by:
)
Hence, we get:

i.e.

Also, let " s " denote the side of the square region.
We know that the perimeter of a square with side " s " is given by:

Now, it is given that:
The perimeters of square region S and rectangular region R are equal.
i.e.

Now, we know that the area of a square is given by:

and

Hence, we get:

and

i.e.

Hence,
Ratio of the area of region R to the area of region S is:

Answer:
1.5 in
Step-by-step explanation:
Let x be the width of the frame.
Side of print=10 in
Area of frame=69 square in
We have to find the width of the frame.
Side of frame=10+x+x=10+2x
Area of square=
By using the formula
Area of print=
Area of frame with print=
Area of frame=Area of frame with print-Area of print




Because Side is always positive.


Hence, width of frame=1.5 in
Value of x is 76°
<u> </u><u>Step-by-step explanation:</u>
Given :- ∠JIH = 107°
and, JDI = 31°
To find :- value of x
solution:- ∠JIH + ∠JID =180° (the sum of angles on a line are supplementary)
∠JID = 180° - 107°
∠JID = 73°
Now in ΔJID
∠JID = 73° and ∠JDI = 31°
by angle some property of Δ
so, ∠JDI + ∠JID + ∠DJI = 180°
= 31° + 73° + ∠DJI = 180°
= 104° + ∠DJI = 180°
∠DJI = 180° - 104°
∠DJI = 76°
now, ∠DJI = ∠AJF = ∠X
so, x = 76°
hence value of x is 76°