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kherson [118]
3 years ago
9

A square and a rectangle have the same area. If the dimensions of the rectangle are 4 ft by 16 ft, how long is a side of the squ

are?
A 10 ft
B. 8 ft
C 32 ft
D. 6ft
E 20 ft
Mathematics
1 answer:
Maru [420]3 years ago
8 0

9514 1404 393

Answer:

  B. 8 ft

Step-by-step explanation:

The area of the rectangle is ...

  A = LW = (16 ft)(4 ft) = 64 ft²

The area of the square in terms of its side length is ...

  A = s²

For the square to have the area of the rectangle, its side length must be ...

  64 ft² = s²

  s = √(64 ft²) = 8 ft

A side of the square is 8 feet long.

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==========================================

Work Shown:

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The reason why RS is equal to RT in the first equation is because we have an isosceles triangle. Recall that any isosceles triangle has exactly two sides the same length, and the opposite base angles are congruent to one another. The congruent angles are indicated with the single arcs.

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