The shaded region in the figure above represents a frame shaped as a

I dont get it.

Question says picture has the same area as the frame itself, but the solution takes the picture area to be 65/2. What am I missing ? question seems to be poorly worded

Let’s let x and y be the lengths of the sides of the picture and c be the length of the hypotenuse of the picture. We have the following two equations:

Area of frame = area of picture

(10 * 13)/2 - xy/2 = xy/2

130 - xy = xy

130 = 2xy

65 = xy

and

x + y = 17

Squaring the above equation, we have:

x^2 + y^2 + 2xy = 17^2

Substituting, we have:

x^2 + y^2 + 2(65) = 289

x^2 + y^2 +130 = 289

x^2 + y^2 = 159

Since x^2 + y^2 = c^2:

c^2 = 159

c = √159

Answer: B

the key first is to nail down the equation and then use the rule that some of 2 sides should be greater than 3rd side the equation being x2 - 17x + 65 = 0 and when we valida/te the same wirh question we get the following option as B bit tricky couldn't pin down under 3 min

The area of the shaded region = the area of the inner triangle

Then the Area of the Inner Right Triangle = (1/2) * (Area of Entire Figure)

= (1/2) * [ (1/2) (10) (13) ]

= 65/2

Let the Legs of the Inner Triangle be X and Y

This means:

(1/2) (X) (Y) = 65/2

Or

XY = 65

Also, based on the Pythagorean Theorem:

(X)^2 + (Y)^2 = (Hypotenuse)^2 = (Z)^2

Question asks for value of Z = ?

We are also given that the 2 legs sum to a value of 17:

X + Y = 17


From here we can use the Square of a Sum quadratic template to find the Hypotenuse of Z

(X + Y)^2 = (X)^2 + (Y)^2 + 2XY

——at this point we can plug in all the information/equations gathered above——


(17)^2 = (Z)^2 + (2) * (65)

(Z)^2 = 289 - 65

Z = sqrt(159)

B

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