Question

The rectangles below have the same perimeter.

Rectangle:A Base=3 height=9
Rectangle B:base=4

Answer 1

**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer:
`\Large\boxed{Area=32~mm^2}`

Explanation:

Given information

Rectangle A:

• Base (b) = 3 mm
• Height (h) = 9 mm

Rectangle B:

• Base (b) = 4 mm
• Height (h) = ?

Both rectangles have the same perimeter

Given formula

1) P = 2 (b + h)

• P = Perimeter
• b = base
• h = height

2) A = b × h

• A = Perimeter
• b = base

• h = height

Find the height of rectangle B

Substitute values into 1) formula to find the perimeter of rectangle A

P = 2 (b + h)

P = 2 (3 + 9)

Simplify by addition

P = 2 × 12

Simplify by multiplication

P = 24 mm

Substitute values into 1) formula to find the perimeter of rectangle B

P = 2 (b + h)

24 = 2 (4 + h)

Divide 2 on both sides

24 / 2 = 2 (4 + h) / 2

12 = 4 + h

Subtract 4 on both sides

12 - 4 = 4 + h - 4

h = 8 mm

Find the area of rectangle B (Purple)

Substitute values into 2) formula

A = b × h

A = 4 × 8

Simplify by multiplication

`\Large\boxed{Area=32~mm^2}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

32 mm²

Explanation:

perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm

length of right rectangle = L

perimeter of right rectangle = 2(L + 4 mm) = 2L + 8

perimeter of right rectangle = 24 mm

The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.

2L + 8 = 24

2L = 16

L = 8

area of right triangle = length × width

area = 8 mm × 4 mm

area = 32 mm²