Solution

Using the Pythagorean Theorem,

The length of the missing leg is \(24\) cm.

Therefore, the perimeter of the triangle is \(7+25+24=56\) cm and the area of the triangle is \(\dfrac{1}{2}(7)(24)=84\) cm².

Solution — Fullscreen

Therefore, the width is \(4x = 4(10.8) = 43.2\) inches and the height is \(3x = 3(10.8) = 32.4\) inches.

The available space is \(45\) inches by \(35\) inches. Therefore, a fullscreen television will fit.

Solution — Widescreen

The width is \(16y =16(2.94\ldots) \approx 47.1\) inches and the height is \(9y = 9(2.94\ldots) \approx 26.5\) inches.

While the height of the television will fit in the space, the width of the television is too big. Robert should not buy a widescreen television.

Square 1

Area of Square 1:

Square 2

Area of Square 2:

Both squares have the same area, so the two expressions must be equal.