Please help me with this question.

Mathematics

1 answer:

earnstyle [38]2 years ago

6 0

Answer: a) 110√2 meters

b) 2.42 hectares

<u>Step-by-step explanation:</u>

a) Since it is a square, the diagonal cuts the square into two 45-45-90 triangles where the diagonal is the hypotenuse. Therefore, the sides are length x and the diagonal is length x√2.

$x\sqrt2=220\\\\\\x=\dfrac{220}{\sqrt2}\\\\\\x=\dfrac{220}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\x=\large\boxed{110\sqrt2}$

b) Area of a square is side squared. 10,000 meters² = 1 hectare

$A=(110\sqrt2)^2\\\\.\quad =(110)^2(\sqrt2)^2\\\\.\quad =12100(2)\\\\.\quad =24200\ \text{meters}^2\\\\.\quad =\large\boxed{2.42\ \text{hectares}}$

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