SOLUTION: Please help: mr. thomas owns a rectangular property that is 52 feet long and 35 feet wide. He adds a new triangular property directly behind his existing property. The base leng

Question 1115045: Please help:
mr. thomas owns a rectangular property that is 52 feet long and 35 feet wide. He adds a new triangular property directly behind his existing property. The base length of the triangular property is equal to the length of the rectangular property. An aerial view of the whole property is shown. The area of the whole property is 2600 square feet. Based on the diagram, what is the maximum height, in feet, of the triangular property
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the rectangular property is 52 long and 35 wide.
the area is therefore 52 * 35 = 1820 square feet.

since the total area of the rectangular property and the triangular property is 2700 square feet, then the triangular property area has to be 2600 - 1820 = 780 square feet.

the base of the triangular property is the same as the length of the rectangular property.

this makes the base of the triangular property 52 feet long.

the area of a triangle is equal to 1/2 * base * height.

base is 52 feet and area is 780 suare feet.

formula becomes 780 = 1/2 * 52 * height

solve for height to get height = 780 / 26 = 30 feet.

that's the height of the triangular property.

1/2 * base * height becomes 1/2 * 52 * 30 which is equal to 780 square feet.

i haven't seen the diagram, but it looks like the height has to be equal to 30 feet.

you have a rectangle that is 52 by 35 which gives an area of 1820 square feet.

you have a triangle that with a base of 52 and a height of 30 which gives an area of 780 square feet.

the total area is 1820 + 780 = 2600 square feet.

RELATED QUESTIONS
Mr.Larsen put a fence around the sides of a rectangular piece of property he owns. If the (answered by Boreal)

find the perimeter of a rectangular playground that is 100 feet wide and 120 feet... (answered by Alan3354)

mr. sill needs to put a fence around his yard. how much fence will he need if the yard is (answered by checkley79)

find the volume of a rectangular prism that is 4 feet high, 6.5 feet wide, and 8 feet... (answered by praseenakos@yahoo.com,jayanthihemkos@yahoo.com)

A farmer is filling in his triangular garden with soil. The garden is 12 feet long and 16 (answered by Alan3354,ikleyn)

Mr. Coleman our principal decided to redesign his rectangular rose bed into the shape of... (answered by venugopalramana)

A rectangular room is 20 feet long and 10 feet wide. If you paint a red rectangle on the... (answered by nerdybill)

what is the perimeter in inches of a rectangular flag that is 4 feet wide and 6 feet... (answered by rfer)

Mr. Thomas is putting up a fence around his field. The field is 360yd long and 225yd... (answered by Theo)