Answer:
The length of the longer ladder is 35 ft
Step-by-step explanation:
Please check the attachment for a diagrammatic representation of the problem
We want to calculate the length of the longer ladder ;
We make reference to the diagram
Since the two right triangles formed are similar. the ratios of their sides are equal;
Thus;
20/15 = 28/x + 15
20(x + 15) = 15(28)
20x + 300 = 420
20x = 420-300
20x = 120
x = 120/20
x = 6
So we want to calculate the hypotenuse of a right triangle with other sides 28ft and 21 ft
To do this, we use the Pythagoras’ theorem which states that square of the hypotenuse equals the sum of the squares of the two other sides
Let the hypotenuse be marked x
x^2 = 28^2 + 21^2
x^2 = 1,225
x = √1225
x = 35 ft
