Question

A piece of cheese is cut into a triangular prism with the cross-section as a right-angled triangle. The sides of the triangle are 2x cm, (4x + 1) cm and (3x + 3) cm. It is given that x > 2. (a) Using Pythagoras’ Theorem, form an equation and show that it reduces to 3x 2 − 10x − 8 = 0.

Answer 1

Explanation:

Tje Pythagoras Theorem states that

`{a}^(2) + {b}^(2) = {c}^(2)`

where and b are the legs

and c is the hypotenuse(the longest side of the right triangle)

The longest side will be 4x+1, and two other sides will lbe 2x, and 3x*+3

So we will get

`(2x) {}^(2) + (3x + 3) {}^(2) = (4x + 1) {}^(2)`

Simplify that, and we get

`4 {x}^(2) + (9 {x}^(2) + 18x + 9) = 16 {x}^(2) + 8x + 1`

`13 {x}^(2) + 18x + 9 = 16 {x}^(2) + 8x + 1`

`0 = 3 {x}^(2) - 10x - 8`