Question

An architectural firm wants to replicate a nearby estate with some changes. 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. What will be the length of the legs of the triangle for the larger estate?

141.42 meters

70.71 meters

100.00 meters

14.14 meters

Answer 1

Option B.

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
`x` 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`

`x^2+x^2=(100)^2`

`2x^2=10000`

Divide both sides by 2.

`x^2=5000`

Taking square root on both sides.

`x=√(5000)`

`x=70.71\text{ meters}`

Hence, the correct option is B.