Question

Two ladders AB and PQ are resting against opposite

walls of an alley. The ladders AB and PQ are 2 m
and 6 m above the ground respectively and T is the
point where the 2 ladders meet.
(i) Given that ATBP is similar to ATAQ, find an
expression, in terms of y, for the length of PA.
(ii) Given that APTM is similar to APQA, find the
length of TM.

Answer 1

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