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ASHA 777 [7]
3 years ago
5

Need help with this math problem

Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Answer: D) The value of \sqrt{215} is between 14.5 and 15

Step-by-step explanation:

Let's start by taking the squaring these numbers.

13^2=169\\13.5^2=182.25\\14^2=196\\14.5^2=210.25\\15^2=225

215 is in between 14.5 squared and 15 squared. That means its square root will be between 14.5 and 15.5

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Step-by-step explanation:

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Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq
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Step-by-step explanation:

Remark

This is one of those questions that can throw you. The problem is that do you include the original rectangle or not. The way it is written it sounds like you shouldn't

However if you don't the question gives you 2 complex answers. (answers with the sqrt( - 1) in them.

Solution

Let the width = x

Let the length = x + 5

Area of the rectangle: L * w = x * (x + 5)

Area of the smaller squares (there are 2)

Area = 2*s^2

x = s

Area = 2 * x^2

Area of the larger squares = 2 * (x+5)^2

Total Area

x*(x + 5) + 2x^2 + 2(x + 5)^2 = 120                 Expand

x^2 + 5x + 2x^2 + 2(x^2 + 10x + 25) = 120     Remove the brackets

x^2 + 5x + 2x^2 + 2x^2 + 20x + 50 = 120      collect the like terms on the left

5x^2 + 25x +  50 = 120                                   Subtract 120 from both sides.

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x^2 + 5x - 14 = 0                                               Factor

(x + 7)(x - 2) = 0                                                 x + 7 has no meaning  

x - 2 =  0

x = 2                                                              

Perimeter

P = 2*w + 2*L

w = 2

L = 2 + 5

L = 7

P = 2*2 + 2 * 7

P = 4 + 14

P = 18

8 0
2 years ago
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