19. The diagonal of a rectangle exceeds the length by 2 cm. If the widthof the rectangle is 10 cm, find the length.20. A cone has base radius 5 cm and slant height 11 cm. Find its vertical height.21. It is possible to find the sides of a right-angled triangle, with lengths which arewhole numbers, by substituting different values of x into the expressions:a) 2x2 + 2x+1b) 2x2 + 2xc) 2x+ 1((a) represents the hypotenuse, (b) and (c) the other two sides.)i) Find the sides of the triangles when x = 1, 2, 3, 4 and 5.ii) Confirm that (2x + 1)² + (2x² + 2x)² = (2x² + 2x+ 1)²22. The diagram represents the starting position (AB) and the• finishing position (CD) of a ladder as it slips. The ladder isleaning against a vertical wall.AGiven: AC=x, OC=4AC, BD=2AC and OB = 5 m.Form an equation in x, find x and hence find the length of theladder.

Answered: Image /qna-images/answer/b3214f34-de3a-418b-8d8e-288a61809533.jpg

Answered: 19. The diagonal of a rectangle exceeds…

19. The diagonal of a rectangle exceeds the length by 2 cm. If the width of the rectangle is 10 cm, find the length. 20. A cone has base radius 5 cm and slant height 11 cm. Find its vertical height.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.CR: Review Exercises

Problem 40CR: Sue and Daves semicircular driveway is to be resealed, and then flowers are to be planted on either...

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Question

19. The diagonal of a rectangle exceeds the length by 2 cm. If the width
of the rectangle is 10 cm, find the length.
20. A cone has base radius 5 cm and slant height 11 cm. Find its vertical height.
21. It is possible to find the sides of a right-angled triangle, with lengths which are
whole numbers, by substituting different values of x into the expressions:
a) 2x2 + 2x+1
b) 2x2 + 2x
c) 2x+ 1
((a) represents the hypotenuse, (b) and (c) the other two sides.)
i) Find the sides of the triangles when x = 1, 2, 3, 4 and 5.
ii) Confirm that (2x + 1)² + (2x² + 2x)² = (2x² + 2x+ 1)²
22. The diagram represents the starting position (AB) and the
• finishing position (CD) of a ladder as it slips. The ladder is
leaning against a vertical wall.
A
Given: AC=x, OC=4AC, BD=2AC and OB = 5 m.
Form an equation in x, find x and hence find the length of the
ladder.

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