The diagonal of a rectangular room is 52 ft long. One wall measures 28 ft longer than the adjacent wall. Find the dimensions of the room.

The dimensions of the rectangular room is 48 ft by 20 ft

Step-by-step 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

a=r

d=q

c=p

b=s

hope this !

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.