The diagram shows a triangular sign advertising fresh pizza slices propped up outside a corner shop. Two equal sides of the sign each measure \(x\) cm, and ...
Question 1 Report
The diagram shows a triangular sign advertising fresh pizza slices propped up outside a corner shop. Two equal sides of the sign each measure \(x\) cm, and the third side measures \(2x - 4\) cm. The perimeter of the sign is 44 cm.
Form an equation in \(x\) and solve it. (3)
Answer Details
The perimeter of a triangle is the sum of its three sides. Writing the two equal sides and the third side as a sum equal to the stated perimeter gives a linear equation in \(x\).
\(x + x + (2x - 4) = 44\)
\(4x - 4 = 44\) (collecting like terms) [1 mark]
\(4x = 48\) (adding 4 to both sides) [1 mark]
\(x = 12\) (dividing both sides by 4) [1 mark]
Checking with \(x = 12\): the two equal sides are each \(12\) cm and the third side is \(2(12) - 4 = 20\) cm, giving a perimeter of \(12 + 12 + 20 = 44\) cm, matching the sign's stated perimeter.
Download The App On Google Playstore
Everything you need to excel in your exams
