Answer:
Length x = 36ft
Breadth y = 15 ft
Therefore, the dimensions of the room x by y is 36ft by 15ft.
Step-by-step explanation:
Let x and y represent the length and breadth of the room
And r represent the diagonal of the room.
Given;
One wall measures 21 ft longer than the adjacent wall
x = y + 21 .......1
The diagonal of a rectangular room is 39 ft long
r = 39ft
Since r is the diagonal, applying Pythagoras theorem;
r = √(x^2 + y^2) = 39
√(x^2 + y^2) = 39
Square both sides and substitute equation 1;
(x^2 + y^2) = 39^2
((y+21)^2 +y^2) = 39^2
(y^2 + 42y + 21^2 + y^2) -39^2 = 0
2y^2 +42y - 1080 = 0
y^2 + 21y - 540 = 0
Solving the quadratic equation, we have;
y = - 39 or y = 15
Since length cannot be negative then;
y = 15 ft
From equation 1;
x = y + 21
x = 15 + 21
x = 36 ft
Length x = 36ft
Breadth y = 15 ft
Therefore, the dimensions of the room x by y is 36ft by 15ft.
