SOLUTION: an equilateral triangle and a rectangle have the same perimeter. the length of a rectangle is 3 cm less tan twice the width. each side of a triangle is 12 cm. find the area of the

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Question 1017069: an equilateral triangle and a rectangle have the same perimeter. the length of a rectangle is 3 cm less tan twice the width. each side of a triangle is 12 cm. find the area of the rectangle.
Found 3 solutions by addingup, ikleyn, MathTherapy:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
The perimeter of the triangle is 12*3=36. And the rectangle has the same perimeter.
and the problem tells us that the length of the rectangle is:
L = 2W-3
Now, the perimeter of the rectangle is:
2L+2W = 36 Substitute for L:
2(2W-3)+2W = 36
4W-6+2W = 36
6W-6 = 36 Add 6, both sides:
6W = 42 Divide both sides by 6
W = 7 This is the width. And the length:
L= 2W-3 = 2(7)-3 = 14-3 = 11 is the length
J
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
An equilateral triangle and a rectangle have the same perimeter. The length of a rectangle is 3 cm less tan twice the width.
Each side of a triangle is 12 cm. find the area of the rectangle.
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The perimeter is 3*12 = 36 cm, calculated for the triangle.

The perimeter of the rectangle is the same: 36 cm.
So, the sum of the measures of two its consecutive sides is  = 18, which gives you an equation

x + y = 18.   (1)

It is the first equation. The second equation is 

x = 2y - 3,   (2)

according to the condition. Substitute the expression (2) into (1) to eliminate x. You will get

2y - 3 + y = 18,  --->  3y = 18+3 = 21  --->  y =  = 7 cm.

Thus one side of the rectangle is 7 cm long.

Then the other side of the rectangle is 18 - 7 = 11 cm.

Then its area is 7*11 = 77 .


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

an equilateral triangle and a rectangle have the same perimeter. the length of a rectangle is 3 cm less tan twice the width. each side of a triangle is 12 cm. find the area of the rectangle.
Area:  

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