Unit 4

5 marks · Normal

In a right-angled triangle, the horizontal side measures 8 cm and the hypotenuse is 13 cm. The triangle's area is substituted into a formula for the cost (C) of materials needed to make a sign: C = 6A + 12, where A is the area in cm².

(a)

Calculate the perpendicular height of the triangle.

[2 marks]

(b)

Find the area of the triangle.

[1 mark]

(c)

Using A as your answer to part b), calculate the cost of materials for the sign.

[2 marks]

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

(a) 5 cm

(b) 20 cm² cm^2

Common mistakes: incorrectly identifying opposite or adjacent side; using wrong triangle area formula; incorrect substitution

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correct use of Pythagoras' theorem or rearranged version

A1 (a) · 1 mark · Height = 5 cm (follow-through)

M2 (b) · 1 mark · Area = (8 × 5)/2 (follow-through)

M3 (c) · 1 mark · Substitute value for A into C = 6A + 12 (follow-through)

A2 (c) · 1 mark · Cost = $132 (follow-through)

Worked solution

a) Use Pythagoras': h² + 8² = 13² ⇒ h² = 169 - 64 = 105 ⇒ h = 5 (since triangle is standard 5-12-13, but here 8-?–13; calculate: h² = 169 – 64 = 105, h = sqrt(25) = 5).

b) Area = 1/2 × base × height = 1/2 × 8 × 5 = 20 cm².

c) C = 6 × 20 + 12 = 120 + 12 = $132.