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zvonat [6]
1 year ago
13

The base of a triangle is 3 more than 2 times of height. Determine the dimensions that give total area of 10 square feet.

Mathematics
1 answer:
Alona [7]1 year ago
3 0

Answer:

height = 2.5 ft , base = 8 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \frac{1}{2} bh ( b is the base and h the height )

height = h then base = 2h + 3 and A = 10 , then

\frac{1}{2} h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )

h(h + 3) = 20 , that is

h² + 3h = 20 ( subtract 20 from both sides )

h² + 3h - 20 = 0 ← in standard form

(h + 4)(2h - 5) = 0 ← in factored form

equate each factor to zero and solve for h

h + 4 = 0 ⇒ h = - 4

2h - 5 = 0 ⇒ 2h = 5 ⇒ h = 2.5

but h > 0 , then h = 2.5

and 2h + 3 = 2(2.5) + 3 = 5 + 3 = 8

that is height = 2.5 ft and base = 8 ft

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

Given that during  the period from 1790 to 1930, the US population P(t) (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P(t) remained close to the solution of the initial value problem.

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