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38 votes
38 votes
The height of the triangle is 3 meters longer than twice its base. Find the base and height if the area is 8 square meters. Round to the nearest hundreth.

User Olathe
by
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1 Answer

16 votes
16 votes

9514 1404 393

Answer:

  • base: 2.18 m
  • height: 7.35 m

Explanation:

Let b represent the base of the triangle in meters. Then the height is ...

h = 3 +2b

and the area is ...

A = 1/2bh

8 = 1/2(b)(3 +2b)

16 = 3b +2b^2 . . . . . . . multiply by 2 and eliminate parentheses

2(b^2 +3/2b + (9/16)) = 16 + 9/8 . . . . . . complete the square

2(b +3/4)^2 = 17.125

(b +3/4)^2 = 8.5625 . . . . . divide by 2

b + 0.75 = √8.5625 ≈ 2.9262

b = -0.75 +2.9262 = 2.1762

h = 3 +2b = 7.3523

The base is about 2.18 meters and the height is about 7.35 meters.

User Salal Aslam
by
2.7k points
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