Answer:
The dimensions of the rectangular room is 48 ft by 20 ft
Explanation:
Drawing a Diagonal line in a rectangle forms two right angle triangles
The diagonal line will represent the hypotenuse
In a right angle triangle:
Hypotenuse^2= adjacent^2+opposite^3
One wall measures 28 ft longer than the adjacent wall.
Let the adjacent=x ft
Opposite=28+x ft
Hypotenuse=52 ft
Hypotenuse^2= adjacent^2+opposite^3
52^2 = x^2 + (28+x)^2
2704 =x^2 + 784 + 56x + x^2
2704=2x^2+784+56x
2x^2+56x+784-2704=0
2x^2+56x-1920=0
Solve the quadratic equation using the quadratic formula
x= -b +or- √b^2-4ac / 2a
a=2
b=56
c=-1920
x= -b +or- √b^2-4ac / 2a
= -56 +or- √56^2 - (4)(2)(-1920) / (2)(2)
= -56 +or- √3136 - (-15,360) / 4
= -56 +or- √3136+15,360) / 4
= -56 +or - √ 18496/ 4
= -56 +or- 136 / 4
x= -56 + 136 / 4
=- 56/4 + 136/4
= -14+34
=20
OR
x= -56 - 136/4
= -56/4 - 136/4
= -14 - 34
= -48
The value of x can't be negative, so will use the positive value of x which is 20
Recall,
Adjacent=x
=20 ft
Opposite=28+x ft
=28+20
=48 ft
The dimensions of the rectangular room is 48 ft by 20 ft