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3 years ago

My friend and I are confused.

Mathematics

1 answer:

Irina-Kira [14]3 years ago

7 0

since the base of the bigger triangle and the base of the smaller triangle are parallel
therefore the two triangle are similar
this means that 10/24=x/3x-3
30x-30=24x "using cross multiplication"
30x-24x=30
6x=30
X=30/6=5

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3 years ago

If the diagonal of a square is approximately 12.73, what is the length of its sides?

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Answer:

The length of the sides of the square is 9.0015

Step-by-step explanation:

Given

The diagonal of a square = 12.73

Required

The length of its side

Let the length and the diagonal of the square be represented by L and D, respectively.

So that

D = 12.73

The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:

$D^{2} = L^{2} + L^{2}$

Solving further, we have

$D^{2} = 2L^{2}$

Divide both sides by 2

$\frac{D^{2}}{2} = \frac{2L^{2}}{2}$

$\frac{D^{2}}{2} = L^2$

Take Square root of both sides

$\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}$

$\sqrt{\frac{D^{2}}{2}} = L$

Reorder

$L = \sqrt{\frac{D^{2}}{2}}$

Now, the value of L can be calculated by substituting 12.73 for D

$L = \sqrt{\frac{12.73^{2}}{2}}$

$L = \sqrt{\frac{162.0529}{2}}$

$L = \sqrt{{81.02645}$

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$L = 9.0015$ (Approximated)

Hence, the length of the sides of the square is approximately 9.0015

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