Question

Ted bought a new TV set. He decided to keep it on a shelf in the corner of the room at some height so that the view gets better. If AB = AC = 48 inches, is the space enough for a TV with an area of the base (as isosceles right triangle shape) equal to 1200 square inches so that no part of the TV lies outside the shelf?

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• A. Yes
• B. No, 48.5

Answer 1

The correct option is B

No, 48.5

The area of the TV is $1200i{n}^2$.

Now, the area of a triangle is half the area of the corresponding parallelogram.

Since it is given that the triangle is right-angled and isosceles, the corresponding parallelogram has adjacent sides equal and all angles are ${90}^{\circ }$.

Thus, the figure is a square.

For the TV to fit in the triangular base, the square must have at least twice the area of the TV.

Thus, the area of the square must be at least $2400i{n}^2$.

Hence, the side of the square must be equal to $\sqrt{2400}=48.89in=49in$.

Thus, AB must have a minimum length of 49 inches.