Question

The diagram shows a rectangle and a triangle.

Rectangle:
2x + 7
X-5
Triangle:
X
2x + 11
2x
The perimeter of the rectangle is equal to the perimeter of the triangle.
Find the value of x.

Answer 1

To determine the value of x, we equate the perimeter of the rectangle to that of the triangle, solve the resulting equation, and find the value of x.

Step-by-step explanation:

To find the value of x, we need to set the perimeter of the rectangle equal to the perimeter of the triangle and solve for x. The perimeter of a rectangle is calculated by adding twice the width and twice the height (P=2l+2w), where l is the length and w is the width. The perimeter of a triangle is the sum of its three sides.

For the rectangle with sides (2x + 7) and (x - 5), the perimeter is 2(2x + 7) + 2(x - 5). For the triangle with sides (x), (2x + 11), and (2x), the perimeter is x + (2x + 11) + 2x. Setting these equal:

2(2x + 7) + 2(x - 5) = x + (2x + 11) + 2x

Solving this equation will give us the value of x.

Answer 2

..perimeter of the rectangle : 2(2x+7+x-5)= 2(3x+2)= 6x+4

perimeter of the triangle : x+2x+11+2x = 5x+11

The perimeter of the rectangle is equal to the perimeter of the triangle.

6x+4=5x+11

we solve for find value of x:

6x-5x=11-4

x=7