E perimeter of a rectangle is 28 meters, and the diagonal is 10 meters,

what is the area?

The rectangle's area is 48 square meters

Step-by-step explanation:

Recall that the perimeter of a rectangle of base b and height h is given by the formula:

Perimeter = 2 b + 2 h

we know that the perimeter is 28 meters, then we can create our first equation;

2 b + 2 h = 28

which means:

2 (b + h) = 28

b + h = 28/2

b + h = 14

the tell us that the diagonal is 10 meters, so we use the Pythagorean theorem to write a second equation using the rectangle's base, height, and diagonal (which form in between the three a right angle triangle where the hypotenuse is the rectangle's diagonal:

So, we can use the equation :  b + h = 14 to write one variable in terms of the other one and use it as substitution in the second (quadratic) equation:

h = 14 - b

then:

which we have reduced at the end by dividing both sides by 2.

we can use factoring to solve these equation;

Se we find two possible solutions: b = 6 m or b = 8 m

If we call b = 8 m, then the height becomes h = 14 - (8) = 6 m

and viceversa.

So a rectangle with such dimensions will render an area that equals :

Area = b x h = 8 x 6 = 48 square meters.

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)