We can use the equation below: a²+b²=c² We use this equation to find c, the diagonal of the triangle or any other missing measurements. We have two bits of information. The larger leg of a right triangle is 2 cm longer than its smaller leg. The smaller leg can be b, while the larger leg is a. We know A=B+2; let's plug that in. (b+2)²+b²=c² The hypotenuse is 4 cm longer than the smaller leg. C=B+4 (B+2)²+b²=(b+4)² Let's get b by itself. B²+4B+4+B²=B²+8B+16 2b²+4b+4=b²+8b+16 Let's subtract 4 from both sides. 2b²+4b=B²+8b+12 Now subtract 8b from both sides. 2b²-4b=B²+12 Now subtract b² from both sides. B²-4B=12 We have our final equation and we need to solve. B²-4B=12 You could plug this into a calculator to find an intersection or you could use math. For me, when I looked at the equation, 6 sprung into my mind and I tested it. 6²-24=12 So, the small leg is 6. If the small leg is 6, the larger leg is 8 since it's 2 more than the small leg. The hypotenuse is 10 since it's 4 more than the small leg. We have 6,8, and 10. To find the perimeter, we just have to add it together. 6+8+10=14+10=24 The perimeter is 24 cm.