Shape and Space 7
3 marks · NormalExplain how you know that two triangles with sides in the ratio 2:3 are similar. Then, if the smaller triangle has an area of 8 cm², find the area of the larger triangle.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
The triangles are similar because their corresponding sides are in the same ratio. The area of the larger triangle is 18 cm².
Also accept: 18cm^2; 18 cm^2
Common mistakes: Multiplying instead of squaring the ratio for areas
Show mark scheme and worked solution
Marking points
B1 · 1 mark · States that the triangles are similar because their corresponding sides are in proportion/ratio.
M1 · 1 mark · Correctly uses (2:3) scale factor to find area ratio: (3/2)^2
A1 · 1 mark · Finds the area of larger triangle as 18 cm².
Worked solution
Triangles with sides in the same ratio are similar (all angles are equal, corresponding sides in proportion).
The ratio of areas = (3/2)^2 = 9/4.
So, area of larger triangle = 8 × 9/4 = 18 cm².