A rectangular card KLMN has KN = 80 cm and KL = 30 cm. Five identical isosceles triangles are cut out along the top edge KN, each with its base on KN. The parts of KN that remain uncut add up to 40 cm. The perimeter of the new shape is 60 cm longer than the perimeter of rectangle KLMN.
- What is the length of the base of each triangle that was cut out?
- What is the perimeter of each isosceles triangle that was cut out?
Need a hint?
Cutting a triangle out of an edge removes its base from the perimeter but adds its two equal sides. Work out how much the perimeter grows for each triangle first.
Worked answer
- (a) Bases of the 5 triangles = 80 cm - 40 cm = 40 cm.
- (a) Each base = 40 cm ÷ 5 = 8 cm.
- (b) Each cut replaces its 8 cm base with two equal sides, so each cut adds (2 × side) - 8 cm to the perimeter.
- (b) Total increase = 60 cm, so each cut adds 60 cm ÷ 5 = 12 cm.
- (b) 2 × side = 12 cm + 8 cm = 20 cm, so each equal side is 10 cm.
- (b) Perimeter of each triangle = 8 cm + 10 cm + 10 cm = 28 cm.
The mistake this question tests
Area and perimeter formulas
Pupils add the whole rectangle's perimeter or use the 60 cm increase as if it were the triangle's perimeter, forgetting that the base is removed from the outline.
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