Annika biked 37 \text{ km}37 km37, start text, space, k, m, end text this morning and another x \text{ km}x kmx, start text, space, k, m, end text in the evening. How many kilometers did Annika bike today?

(37 + x) km

Step-by-step explanation:

To know the number of kilometers biked by Annika today, we need to add what she biked in the morning to what she biked in the evening.

From the question, she biked 37 km in the morning and x km in the evening

So the total distance biked by Annika today will be (37 + x) km

0,0

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240