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Fudgin [204]
3 years ago
14

The height of a triangle is 2 less than 5 times its base. If the base of the triangle is xfeet, and the area is 12 square feet,

which equation mofles this situation
Mathematics
1 answer:
Reil [10]3 years ago
6 0

Answer:

5B^{2}  - 12B +10B - 24 = 0\\\\\   Base of triangle = 2.4 Feet and Height of triangle = 10 feet.

Step-by-step explanation:

This problem can be solved by using formula to calculate area of triangle.

<u>Area of triangle = 1/2*(base*height)</u>

given

Let base of triangle B

height if triangle H

according to problem

The height of a triangle is 2 less than 5 times its base

mathematically it can be expressed as

H = 5*B - 2

Given area of triangle= 12 sq feet

Area of triangle = 1/2*(base*height)

=> 12 = 1/2* {B*(5*B-2)}

=> 24 = 5B^2 - 2B

5B^{2}  - 12B +10B - 24 = 0\\\\\   which is a  quadratic equation

It can be solved as given below

5B^{2}  +10B - 12B  - 24 = 0\\\\\=>5B(B +2) -12(B +2) = 0\\=> (5B - 12) (B +2) = 0\\5B - 12 = 0      or B + 2 = 0\\Hence B = 12/5 \  or  \ B = -2\\\\  

Since for side of triangle B cannot be negative number hence B= 12/5 = 2.4

Therefore height of triangle = 5*B - 2 = 5*2.4 - 2 = 12 - 2 = 10

Base of triangle = 2.4 Feet and Height of triangle = 10 feet.

Equation which models this situation is

5B^{2}  - 12B +10B - 24 = 0\\\\\

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