Congratulations to our Sixth Year Maths quiz winners: Laragh Mai Carrigan, Amy Feighan, Iseult Mason, Katie Ferris, Aine Ni Riain
•Lets take that one of the sides is x cm. (x > 3), then the other will be x – 3 cm. For the surface we find S1 = x(x – 3) cm2. If we increase the proportions by 1cm. the sides will be (x + 1) cm.
• (x – 3 + 1 ) = (x – 2) cm. and these are the new proportions of the rectangle so the surface is S2 = (x + 1).(x – 2) cm2. It is 18 cm2 bigger than the first one. Therefore we get the following equation:
S1 +18 = S2 <=> x(x – 3) + 18 = (x + 1)(x – 2) <=> x2 – 3x + 18 = x2 + x – 2x – 2 <=> 2x = 20 <=> x = 10. So the sides of the rectangle are 10 cm. and (10 – 3) = 7cm.
A school bus travels from Veldhoven to Roosendaal. There are four children on the bus. Each child has four backpacks with him. There are four dogs sitting in each backpack. Every dog has four puppies with her. All these dogs have four legs, with four toes on each paw.
What is the total number of toes in the bus?