Part A; The height of the base is 15 cm.
Part B; Approximately 320 cm of cardboard is used to make the candy box.
Step-by-step explanation:
Step 1; We split the triangle into two right-angled triangles. So each triangle has an 8 cm long adjacent side and a 17 cm long hypotenuse. As we have two sides of the triangle, we can solve for the other side's length by using Pythagoras' theorem. Assume the opposite side of the triangle measures x cm. According to Pythagoras theorem, 17² = 8² + x²,
289 = 64 + x², x² = 289 - 64 = 225, x = √225 = 15 cm.
So the height of the base is 15 cm.
Step 2; To find the amount of cardboard needed, we need to determine the perimeter. There are 2 triangular faces and 3 rectangular faces.
A triangle's perimeter is the sum of all the side lengths.
The perimeter of the triangular face = 16 + 17 + 17 = 50 cm.
The perimeter for two triangular faces = 2 × 50 = 100 cm.
Step 3; A rectangle's perimeter is determined by multiplying the rectangle's length with the rectangle's width.
Of the three rectangular faces, two are similar.
The perimeter for the face along the side of the triangle = 2 × (20 + 17) =
2 × 37 = 74 cm.
The perimeter for two similar rectangular planes = 2 × 74 = 148 cm.
The perimeter for the face along the base of the triangle = 2 × (16 + 20) =
2 × 36 = 72 cm.
The perimeter of the entire shape = 100 + 148 + 72 = 320 cm.
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