Question

Find the value of x so that the figures have the same perimeter... #9

Answer 1

A , x = 4

The perimeter of the triangle = 5x + 1 +2x + 5 + 3x + 4 = 10x + 10

The perimeter of the rectangle = 2x + 2x + x + 13 + x + 13 = 6x + 26

Equating the 2 perimeter expressions

10x + 10 = 6x + 26 ( subtract 6x from both sides )

4x + 10 = 26 ( subtract 10 from both sides )

4x = 16 ( divide both sides by 4 )

x = 4 → A

Answer 2

The perimeter of a shape is the sum of side lengths of the shape.

The value of x so that they have the same perimeter is 4

The perimeter of the triangle is calculated as follows:

$P_1 = 3x + 4 + 5x + 1 + 2x + 5$

Collect like terms

$P_1 = 3x + 5x + 2x+ 4 + 1 + 5$

$P_1=10x + 10$

The perimeter of the rectangle is calculated as follows:

$P_2 = 2 \times (2x + x + 13)$

$P_2 = 2 \times (3x + 13)$

Open brackets

$P_2 = 6x + 26$

When they have the same perimeter;

$P_1= P_2$

So, we have:

$10x + 10 = 6x + 26$

Collect like terms

$10x - 6x = 26 - 10$

$4x = 16$

Divide by 4

$x = 4$

Hence, the value of x is 4

Read more about perimeters at:

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