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.
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