77.9k views
5 votes
the base of a triangle is 7 less than twice its height. If the area of the triangle is 102m^2, find the length of the base.

User Eran Meiri
by
8.3k points

1 Answer

4 votes

Answer:

The length of the base will be: 17 m

Explanation:

Given the area of the triangle


A=102\:m^2

Using the formula of Area of a triangle:


A=(1)/(2)\left(b* h\right)

Here,

  • 'b' is the base
  • 'h' is the height

As the base of a triangle is 7 less than twice its height.

so


b=2h-7

so the formula of Area of a triangle becomes


102=(1)/(2)\left(\left(2h-7\right)* \:h\right)


204=h\left(2h-7\right)


2h^2-7h=204


2h^2-7h-204=0


\left(2h+17\right)\left(h-12\right)=0


2h+17=0\quad \mathrm{or}\quad \:h-12=0


h=-(17)/(2),\:h=12

As height can not be negative, so:


h=12 m

Hence, the length of the base:


b=2h-7


= 2(12)-7


=24-7


= 17 m

Therefore, the length of the base will be: 17 m

User Gertjan Brouwer
by
7.8k points

Related questions

1 answer
4 votes
77.2k views
asked May 19, 2024 132k views
SaleCar asked May 19, 2024
by SaleCar
7.6k points
1 answer
5 votes
132k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories