Question

Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x and y vary with time. If x increases at a constant rate of 19 ft/s and y decreases at a constant rate of 15 ft/s, how fast is the size of the diagonal changing when x

Answer 1

The rate of change of the size of the diagonal is; 25.2 ft/s

By Pythagoras theorem;

The length, l of a diagonal of a rectangle whose sides have lengths x and y is;

• l² = x² + y².

In essence; the length of the diagonal is dependent on the length, x and y of the sides.

Therefore;

(dl/dt)² = (dx/dt)² + (dy/dt)²

where;

• (dx/dt) = 19 ft/s
• (dy/dt) = -15 ft/s

Therefore,

(dl/dt)² = 19² + (-15)²

(dl/dt)² = 361 + 225

dl/dt = √586

dl/dt = 25.2

Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.

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