Math worksheet for 7th grade students focusing on finding missing sides of similar figures using proportions.

I'll solve each problem step by step, finding the missing side using proportions for similar figures.

Problem 1:
Large rectangle: 48 × 40
Small rectangle: 12 × x

Setting up proportion: 48/12 = 40/x
4 = 40/x
x = 40/4 = 10

Problem 2:
Small rectangle: 3 × 2
Large rectangle: x × 10

Setting up proportion: 3/x = 2/10
Cross multiply: 3(10) = 2(x)
30 = 2x
x = 15

Problem 3:
Large rectangle: 108 × 81
Small rectangle: x × 9

Setting up proportion: 108/x = 81/9
108/x = 9
x = 108/9 = 12

Problem 4:
Small rectangle: 6 × x
Large rectangle: 72 × 54

Setting up proportion: 6/72 = x/54
Cross multiply: 6(54) = 72(x)
324 = 72x
x = 324/72 = 4.5

Problem 5:
Large rectangle: 72 × 60
Small rectangle: 6 × x

Setting up proportion: 72/6 = 60/x
12 = 60/x
x = 60/12 = 5

Problem 6:
Large rectangle: 20 × x
Small rectangle: 4 × 10

Setting up proportion: 20/4 = x/10
5 = x/10
x = 50

Problem 7:
Large triangle: base 36, side 44
Small triangle: base 9, side x

Setting up proportion: 36/9 = 44/x
4 = 44/x
x = 44/4 = 11

Problem 8:
Large triangle: base 24, side 22
Small triangle: base 12, side x

Setting up proportion: 24/12 = 22/x
2 = 22/x
x = 22/2 = 11

Final Answer:
1) x = 10
2) x = 15
3) x = 12
4) x = 4.5
5) x = 5
6) x = 50
7) x = 11
8) x = 11