# NCERT Exemplar Solutions Class 8 Mathematics Solutions for Squares and Square Roots & Cubes and Cube Roots - Exercise in Chapter 3 - Squares and Square Roots & Cubes and Cube Roots

Question 128 Squares and Square Roots & Cubes and Cube Roots - Exercise

A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. Find the distance between the wall and the foot of the ladder.

Let us consider the right angle triangle PQR

Given,

Long ladder i.e. RQ = 5.5 m

The ladder reaches the wall to a height i.e. PR = 4.4 m

From Pythagoras theorem,

\begin{array}{l} \mathrm{RQ}^{2}=\mathrm{RP}^{2}+\mathrm{PQ}^{2} \\ 5.5^{2}=4.4^{2}+\mathrm{PQ}^{2} \\ \mathrm{PQ}^{2}=5.5^{2}-4.4^{2} \\ \mathrm{PQ}=\mathrm{V}\left(5.5^{2}-4.4^{2}\right) \\ \mathrm{PQ}=\mathrm{V}(30.25-19.36) \\ \mathrm{PQ}=\sqrt{10.89} \end{array}

PQ = 3.3

∴ The distance between the wall and the foot of the ladder is 3.3 m.

Video transcript
hello students welcome to lino q a video session i am saf your math tutor and question for today is a 5.5.5 meter long ladder is lean against a wall the ladder reaches the wall to the height of 4.4 meter find the distance between the wall and the foot of the ladder so let us see what is given first of all we have been given that from the figure you can see the ladder rq is 5.5 meter the ladder reaches the wall to the height of pr which is 4.4 meter now from pythagoras theorem pythagoras theorem says that in right triangle rbq we have rq square is equal to rp square plus pr square rq square is equal to rp square plus pq square so rq here is 5.5 5.5 square is equal to 4.4 square plus pq square here we need to find pq so pq is equal to under root of 5.5 square minus 4.4 square so pq is equal to under root of 30.25 minus 19.36 pq value comes out to be root of 10.89 now to find the root of 10.89 we must use the long division method so ten point eight nine group it from here and then you have to make the square which is nearest to the ten three threes are nine one and here three plus three is six six one more time and then eighty nine point eight nine will go down or you cannot you can make a point over here and 89 now after the sixth place here we need to select one digit which is which which will be multiplied with some number the same number to have the nine at its place so here we should select a digit in such a way that it should be 3 into 3 which is 9 and 189 exact so here you will get reminder to be zero hence your root of n point eight nine is three point three so p q value is equal to three point three meter this is the required distance between the wall and the foot of the ladder if you have any queries you can drop it in comment section and subscribe to lido for more q a thank you for watching
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