Question

Help! Last question

A rectangle is 5 feet wide and 3x – 5 feet long. It has the same area as a triangle with a height of 10 feet and a base of x + 3 feet. What is the area of the triangle?

Area of rectangle: A=lw Area of triangle: A=12bh

x = ?
Area of triangle = ?

Answer 1

x=4

Area of triangle=35 square feet

Explanation:

Before I start the Area of triangle=1/2(bh) not 12bh.

From the question lw=1/2(bh)

and l=3x-5,w=5, b=x+3 and h=10

So the equation is 5(3x-5)=1/2(10(x+3))

since lw=wl and bh=hb

Then 15x-25=1/2(10x+30) and the LCM is 2 so multiply both sides by 2

2(15x-25)=2(1/2(10x+30)

30x-50=10x+30 since 1/2 eliminates 2

grouping like terms,

30x-10x=30+50

20x=80, dividing both sides by 20

x=4

Area of triangle=1/2(bh)

=1/2(10(x+3)) by inserting the value of x into the equation,

1/2(10(x+3))=1/2(10(4+3))

=1/2(10(7))

=1/2(70)

=35

So the answer is 35 square feet