Answer:
Step-by-step explanation:
Let X designate the point at the lower left front corner of the room shown. Then BX is the edge marked "length." The Pythagorean theorem applied to right triangle BXC tells you ...
BC² = BX² + XC²
Applied to right triangle ACB, the Pythagorean theorem tells you ...
AB² = AC² + BC²
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We can use the first of these equations to find BC. Filling in the given numbers for BX = length = 20 ft and XC = width = 48 ft, we have ...
BC² = (20 ft)² + (48 ft)² = (400 +2304) ft² = 2704 ft²
BC = √2704 ft
BC = 52 ft
Using the height and the value for BC² in the second equation, we get ...
AB² = (10 ft)² + 2704 ft²
AB² = 2804 ft²
AB = √2804 ft ≈ 52.9528 ft
AB ≈ 53.0 ft
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You may have noticed that when we substitute for BC² in the second equation, the square of the length of the space diagonal (AB) has the equation ...
AB² = AC² + XC² +BX² . . . . the sum of the squares of length, width, height
