The diagonal of a rectangular room is 39 ft long. One wall measures 21 ft longer than the adjacent wall. Find the dimensions of the room.

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.

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