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Chapter 10: Q52. (page 659)

A ladder is leaning on a building. The base of the ladder is 10 feetfrom the building, and the ladder reaches up 15 feeton the building. How long is the ladder?

Short Answer

Expert verified

The ladder is513 feet long

Step by step solution

01

Step 1. Given. 

The base of the ladder=10feet

The ladder reaches up to a height of 15 feet

02

Step 2. Draw the rough sketch for the given problem.

The rough sketch for the given problem is:

ACis the building andCE is the ground.

BCis the height up to which ladder can reach on the building.

CDis the distance of the base of the ladder from the building.

BDis the ladder.

03

Step 3. Determine the length of the ladder.

In the triangle BCD,鈭�BCD is a right angle. Therefore, the triangleBCD is right-angled.

According to the Pythagorean theorem, it can be noticed that:

BD2=BC2+CD2

Therefore,

BD2=BC2+CD2BD2=152+102BD2=225+100BD2=325BD=325BD=25脳13BD=52脳13BD=513

Therefore, the ladder is513 feet long.

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