Geometry word problem?

Question

A diagonal walk through a small rectangular garden 9 meters by 12 meters can be built at $10 per linear meter. How much will the walk cost.

How do I set this up and solve it?

Answer 1

To simply answer this question, we know that a right angle triangle with an adjacent side of 3 and an opposite side of 4, will have an hypotenuse of 5. This is known as an 3,4, 5 triangle, multiplies of this will also be right angled triangles, so that, 6,8, 12; 9, 12 and 15 would also be.

This tell you without doing any form of calculation that the diagonal walk would be 15m, giving a cost of $150.

Answer 2

The diagonal of a rectangle is the hypotenuse of the resulting two triangles. Use the Pythagorean theory formula to find the length of the diagonal, which I shall name x.

9² + 12² = x² = 81 + 144

x² = 225 Now get the square root of 225

x = 15 meters

Since the diagonal walk costs $10 per linear meter, the cost is $150.

Answer 3

The garden has right angles in the corners. Draw the rectangle, and then draw the diagonal line through it. Now you have a right triangle. Use the Pythagorean Theorem.

A² + B² = C²

9² + 12² = C²

81 + 144 = C²

C² = 225

C = 15

At $10 per linear meter, that would be $150 total.

Answer 4

The diagonal walkway is the hypotenuse of a right triangle whose legs are 9 and 12. By the pythagorean theorem the hypotenuse is equal to the square root of the sum of the squares of the legs.

Thus d = sqrt(9^2+12^2) = 15 meters
So cost = 15*10 = $150.

Answer 5

The first thing you should do with any math problem with that type of wording is to draw or sketch the diagram on a piece of paper. You should have a rectangle with a line straight from the top left hand corner going straight to the bottom right hand corner to represent the 'walk'. ( the line can also be vice versa.) Now you can see that the rectangle is divided into two triangles and you have the lengths of the two outer sides. What you need to find is the length of the long inner line called the hypotenuse. y ou do this by using Pythagoras' theorem which states that: a(squared)=b(squared)+c(squared). You then need to substitute the values that you have for the sides that you already have, thatis the 9 and 12 metres( they will be the constants b and c. When you square them both and add them together as the problem states you will obtain the square of the line that you are trying to find. You now need to find the square root of your answer and that will be the length of the line or the 'walk' of the garden. The answer you obtain you now multiply it by $10.00 to obtain the cost of the walk.
Let me simplify:-
Using Pythagoras' theorem
a(squared)=b(squared)+c(squared)
a(squared)=(9*9)+(12*12)
a(squared)=(81)+(144)
a(squared)=225
a=square root of 225=15m
Cost=15m$10.00
=$150.00

Answer 6

draw a sketch of the garden
What is a diagonal in relation to a rectangle?
draw in the diagonal
how long is the diagonal
cost = rate per meter * length in meters