Question

Please answer these 2 and please give an explanation so i can learn it. Thanks

Answer 1

Question (4):

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Formula
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a² + b² = c²

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Substitute the values and solve the unknown
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4² + 3² = c²
c² = 16 + 9
c² = 25
c = √25
c = 5

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Answer: 5 inches
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Question (5):

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Given information
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Area of a square = 25m²

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Find length
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Area of a square = Length x Length
Length² = 25
Length = √25
Length = 5m

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Find Diagonal
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a² + b² = c²
5² + 5² = c²
c² = 25 + 35
c² = 50
c = √50
c = 5√2 (Radical Form) or 7.07 (rounded to nearest hundredth)

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Answer: Diagonal = 7.07m
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Answer 2

4.

The formula for the diagonal of a rectangle is:


`\sf D=√(l^2+w^2)`

Plug in what we know:


`\sf D=√(4^2+3^2)`

Simplify the exponents:


`\sf D=√(16+9)`

Add:


`\sf D=√(25)`

Take the square root:


`\sf D=\boxed{\sf 5~in}`

For the second one, we know that the area of a square is:


`\sf A=s^2`

Plug in what we know:


`\sf 25=s^2`

Take the square root of both sides:


`\sf s=5`

So we know that the length and width are both 5 meters long, let's plug this into the formula for the diagonal:


`\sf D=√(5^2+5^2)`

Simplify the exponents:


`\sf D=√(25+25)`

Add:


`\sf D=√(50)`

Take the square root:


`\sf D\approx\boxed{\sf 7.07~m}`