The larger leg of a right triangle is 2 cm longer than its smaller leg. the hypotenuse is 4 cm longer than the smaller leg . what is the perimeter of the trianglw

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.

Definitely