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.

the answer is b.)

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