Pole In The Van (3D Pythag)

Difficulty:
intermediate

Rating:
4-stars

GCSE Marks:
4-marks

GCSE Text:
Gino needs to fit some long poles into a van that he has hired.  The poles are 2.7m in length. The dimensions of Gino’s van are:

Hire Van

a)  Will the poles fit diagonally across the floor of the hire van?

b)  If not, is there another way that Gino could fit the poles into the van and successfully close the doors?

Suggestions:
This is a typical GCSE problem where the method is not mentioned in the text.  This problem requires students to visualise a 2D triangle from a 3D drawing, but once identified, students usually select the correct method to solve this problem in about 4-5 minutes. It often helps for students to sketch 2D triangles in order to calculate side lengths correctly.

Extension Ideas:
Teachers could extend the learning by considering:

  • A larger van was available to hire which measured the same width, but which was 20% longer and 10% higher.  What would be the maximum pole length (to 1 d.p.) that could fit into this larger van?

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