An architect sketches the cross-section of a pitched roof as an isosceles triangle…
MATHEMATICS · Subjective · GCSE · Mathematics · Ratio and Proportion · Ratio and Proportion
Problem
An architect sketches the cross-section of a pitched roof as an isosceles triangle whose base is 8 cm and each equal side is 10 cm on the drawing.
The roof must finally span a hall that is exactly 20 m wide.
a) Find the scale of the drawing by comparing the width of the hall with the base of the triangle on the sketch.
b) Determine the actual length of each of the equal sides of the roof, giving your answer correct to the nearest centimetre.
c) In the completed roof a triangular opening is formed by joining the mid-points of the three actual rafters (the sides of the big triangle). Prove that this opening is similar to the whole roof triangle and calculate the perimeter of the opening in metres.