3. In a figure a small square is cutting out from the largesquare. The area of the remaining part is 91 cm². The sum of Sides equal to 52cm. (a). If the side of large square is x and the side of smallest square is y then find the area of the remaining part?
(b). Find the sides of the smallest square?
(c). Find the areas of the two squares?

Step-by-step explanation:

Given that,

Further given that,

It means

We know,

So, using this, we have

Now, Further given that,

If square EFGH is cutting out from square ABCD, the area of remaining part is 91 square cm.

It means

We know,

So, using this, we get

can be further rewritten as using algebraic Identity,

On adding equation (1) and (2), we get

On substituting the value of x in equation (1), we have

So,

and

Also,

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c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)