Answer:
Option B.
Step-by-step explanation:
It is given that the new estate will be larger than the original by a scale factor of 1:10.
A section of the roof in the original estate is constructed using 45-45-90 triangles. The hypotenuse of the triangle is 10 meters long.
Two angles are equal and one angle is a right angle, it means it is an isosceles right-angled triangle.
Let
be the length of the legs of the triangle for the larger estate.
The hypotenuse of larger estate = 10 × 10 = 100
Using Pythagoras triangle,
![perpendicular^2+base^2=hypotenuse^2](https://tex.z-dn.net/?f=perpendicular%5E2%2Bbase%5E2%3Dhypotenuse%5E2)
![x^2+x^2=(100)^2](https://tex.z-dn.net/?f=x%5E2%2Bx%5E2%3D%28100%29%5E2)
![2x^2=10000](https://tex.z-dn.net/?f=2x%5E2%3D10000)
Divide both sides by 2.
![x^2=5000](https://tex.z-dn.net/?f=x%5E2%3D5000)
Taking square root on both sides.
![x=\sqrt{5000}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B5000%7D)
![x=70.71\text{ meters}](https://tex.z-dn.net/?f=x%3D70.71%5Ctext%7B%20meters%7D)
Hence, the correct option is B.
<span>10(2y+2)−y=2(8y−8)
=
12-</span>